CMPINF-2100 Final Project

Spotify Song Popularity – Regression Analysis

This notebook follows the project structure:

1. Introduction
2. EDA
3. Clustering
4. Models: Fitting and Interpretation
5. Models: Predictions
6. Models: Performance and Validation

We use the TidyTuesday Spotify dataset (2020-01-21) and treat track_popularity as a continuous response variable (regression).

Import Modules

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.compose import ColumnTransformer
from sklearn.cluster import KMeans
from sklearn.model_selection import train_test_split, KFold, cross_val_score
from sklearn.pipeline import Pipeline
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score, mean_squared_error

import statsmodels.formula.api as smf

Read data

songs_url = 'https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2020/2020-01-21/spotify_songs.csv'
spotify = pd.read_csv(songs_url)

1. Introduction

We analyze the Spotify songs dataset from the TidyTuesday project (2020-01-21) as a regression problem. The response is track_popularity (0–100).

Goal: Understand and predict how audio characteristics (e.g., danceability, energy, valence), song characteristics (duration_ms, tempo), and contextual information (playlist_genre, playlist_subgenre, release_year) relate to track popularity as a continuous variable ( regression problem).

High-level summary of findings (to be completed after analysis): Which inputs/features seem to influence the response/outcome the most? What supported your conclusion? Was it only through predictive models?

• Artist popularity, artist hit rate, playlist popularity are significant predictors of popular tracks
• There are some subgenres like pop teen that significantly increase the odd of track being popular.
• There are audio characteristics, that when interacted with the significant predictors mentioned above, which increase the odd of track being successful, such as danceability, energy, and instrmentalness.
• This will be seen below from the multiple regression that have been tested. It will also show through the EDA section.

Was clustering consistent with any conclusions from the predictive models?

• Clustering supported the notion that popular tracks are driven by artist related and playlist related features.

iWhat skills did you learn from going through this project?

• I have learned many valuable skills including:

  • Data Analysis
  • Programming
  • Data Vizualization
  • Modelling

• This project have made me greatly progress in the aquistiion and mastery of data science.

EDA

Basic Information

spotify.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 32833 entries, 0 to 32832
Data columns (total 23 columns):
 #   Column                    Non-Null Count  Dtype  
---  ------                    --------------  -----  
 0   track_id                  32833 non-null  object 
 1   track_name                32828 non-null  object 
 2   track_artist              32828 non-null  object 
 3   track_popularity          32833 non-null  int64  
 4   track_album_id            32833 non-null  object 
 5   track_album_name          32828 non-null  object 
 6   track_album_release_date  32833 non-null  object 
 7   playlist_name             32833 non-null  object 
 8   playlist_id               32833 non-null  object 
 9   playlist_genre            32833 non-null  object 
 10  playlist_subgenre         32833 non-null  object 
 11  danceability              32833 non-null  float64
 12  energy                    32833 non-null  float64
 13  key                       32833 non-null  int64  
 14  loudness                  32833 non-null  float64
 15  mode                      32833 non-null  int64  
 16  speechiness               32833 non-null  float64
 17  acousticness              32833 non-null  float64
 18  instrumentalness          32833 non-null  float64
 19  liveness                  32833 non-null  float64
 20  valence                   32833 non-null  float64
 21  tempo                     32833 non-null  float64
 22  duration_ms               32833 non-null  int64  
dtypes: float64(9), int64(4), object(10)
memory usage: 5.8+ MB

spotify.dtypes

track_id                     object
track_name                   object
track_artist                 object
track_popularity              int64
track_album_id               object
track_album_name             object
track_album_release_date     object
playlist_name                object
playlist_id                  object
playlist_genre               object
playlist_subgenre            object
danceability                float64
energy                      float64
key                           int64
loudness                    float64
mode                          int64
speechiness                 float64
acousticness                float64
instrumentalness            float64
liveness                    float64
valence                     float64
tempo                       float64
duration_ms                   int64
dtype: object

spotify.isna().sum().sort_values(ascending=False)

track_artist                5
track_album_name            5
track_name                  5
track_id                    0
key                         0
tempo                       0
valence                     0
liveness                    0
instrumentalness            0
acousticness                0
speechiness                 0
mode                        0
loudness                    0
danceability                0
energy                      0
playlist_subgenre           0
playlist_genre              0
playlist_id                 0
playlist_name               0
track_album_release_date    0
track_album_id              0
track_popularity            0
duration_ms                 0
dtype: int64

spotify.nunique().sort_values(ascending=False)

track_id                    28356
track_name                  23449
track_album_id              22545
duration_ms                 19785
track_album_name            19743
tempo                       17684
track_artist                10692
loudness                    10222
instrumentalness             4729
track_album_release_date     4530
acousticness                 3731
liveness                     1624
valence                      1362
speechiness                  1270
energy                        952
danceability                  822
playlist_id                   471
playlist_name                 449
track_popularity              101
playlist_subgenre              24
key                            12
playlist_genre                  6
mode                            2
dtype: int64

spotify["track_album_release_date"] = pd.to_datetime(
    spotify["track_album_release_date"], errors="coerce"
)
spotify["release_year"] = spotify["track_album_release_date"].dt.year
spotify["release_month"] = spotify["track_album_release_date"].dt.month

b. Visualization

continuous_vars = [
    "danceability", "energy", "loudness", "speechiness",
    "acousticness", "instrumentalness", "liveness", "valence",
    "tempo", "duration_ms"
]

categorical_vars = ["playlist_genre", "playlist_subgenre", "mode","key"]

vars_to_plot = ["track_popularity", "danceability", "energy", "valence", "duration_ms"]

1. Counts of categorical variables

sns.catplot( data = spotify , kind = 'count', x = 'playlist_genre',aspect=1.5)
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

sns.catplot( data = spotify , kind = 'count', x = 'playlist_subgenre', aspect = 6)
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

plt.figure(figsize=(10, 4))
sns.countplot(data=spotify, x="playlist_subgenre", order=spotify["playlist_subgenre"].value_counts().index[:10])
plt.xticks(rotation=45)
plt.title("Counts of top 10 playlist_subgenre")
plt.tight_layout()
plt.show()

2. Distributions of continuous variables

spotify_lm = spotify.reset_index().rename(columns={'index':'row_id'}).melt(id_vars=categorical_vars, value_vars=continuous_vars)

sns.displot( data = spotify_lm , x = 'value', col = 'variable', kind = 'hist', aspect = 2, col_wrap=3, facet_kws={'sharex': False, 'sharey': False}, common_bins=False, kde=True)
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

plt.figure(figsize=(14, 8))
for i, var in enumerate(vars_to_plot, start=1):
    plt.subplot(2, 3, i)
    sns.histplot(data=spotify, x=var, bins=30, kde=True)
    plt.title(var)
plt.tight_layout()
plt.show()

3. Relationships between continuous variables

corr_cols = ["track_popularity"] + continuous_vars
corr = spotify[corr_cols].corr()

plt.figure(figsize=(10, 8))
sns.heatmap(corr, cmap="coolwarm", center=0,annot=True,vmin=-1,vmax=1)
plt.title("Correlation heatmap: popularity and continuous features")
plt.tight_layout()
plt.show()

This corr plot summarizes the relationship between the continious variables. Track popularity is not strongly correlated with any 'one' audio characetristic.

sns.pairplot(spotify[continuous_vars + ["track_popularity"]],diag_kws={'common_norm':False})
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

sample_df = spotify.sample(5000, random_state=0)

plt.figure(figsize=(15, 4))
for i, var in enumerate(["danceability", "energy", "valence"], start=1):
    plt.subplot(1, 3, i)
    sns.scatterplot(data=sample_df, x=var, y="track_popularity", alpha=0.3)
    plt.title("Popularity vs " + var)
plt.tight_layout()
plt.show()

4. Summaries of the continuous variables grouped by categorical variables

sns.catplot(data = spotify, x="playlist_genre", y="track_popularity", kind="box", aspect=1.5)
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

--- 2.7 Summaries grouped by categorical variables ---

group_summary = (
    spotify
    .groupby("playlist_genre")[["track_popularity"] + continuous_vars]
    .mean()
    .sort_values("track_popularity", ascending=False)
)

group_summary

	track_popularity	danceability	energy	loudness	speechiness	acousticness	instrumentalness	liveness	valence	tempo	duration_ms
playlist_genre
pop	47.744870	0.639302	0.701028	-6.315328	0.073991	0.170794	0.059876	0.176833	0.503521	120.743178	217768.104231
latin	47.026576	0.713287	0.708312	-6.264455	0.102653	0.210920	0.044447	0.180626	0.605510	118.622354	216863.446945
rap	43.215454	0.718353	0.650708	-7.042269	0.197506	0.192479	0.075997	0.191654	0.505090	120.654908	214163.889140
rock	41.728338	0.520548	0.732813	-7.588895	0.057696	0.145189	0.062417	0.203135	0.537352	124.988786	248576.500303
r&b	41.223532	0.670179	0.590934	-7.864848	0.116792	0.259904	0.028920	0.175268	0.531231	114.222156	237599.489781
edm	34.833526	0.655041	0.802476	-5.427445	0.086695	0.081504	0.218578	0.211859	0.400656	125.768024	222540.858349

spotify\
    .groupby(["playlist_genre"])[["track_popularity"]+continuous_vars]\
    .mean().reset_index().sort_values("track_popularity", ascending=False)

	playlist_genre	track_popularity	danceability	energy	loudness	speechiness	acousticness	instrumentalness	liveness	valence	tempo	duration_ms
2	pop	47.744870	0.639302	0.701028	-6.315328	0.073991	0.170794	0.059876	0.176833	0.503521	120.743178	217768.104231
1	latin	47.026576	0.713287	0.708312	-6.264455	0.102653	0.210920	0.044447	0.180626	0.605510	118.622354	216863.446945
4	rap	43.215454	0.718353	0.650708	-7.042269	0.197506	0.192479	0.075997	0.191654	0.505090	120.654908	214163.889140
5	rock	41.728338	0.520548	0.732813	-7.588895	0.057696	0.145189	0.062417	0.203135	0.537352	124.988786	248576.500303
3	r&b	41.223532	0.670179	0.590934	-7.864848	0.116792	0.259904	0.028920	0.175268	0.531231	114.222156	237599.489781
0	edm	34.833526	0.655041	0.802476	-5.427445	0.086695	0.081504	0.218578	0.211859	0.400656	125.768024	222540.858349

spotify\
    .groupby(["playlist_subgenre"])[["track_popularity"]+continuous_vars]\
    .mean().reset_index().sort_values("track_popularity", ascending=False)

	playlist_subgenre	track_popularity	danceability	energy	loudness	speechiness	acousticness	instrumentalness	liveness	valence	tempo	duration_ms
17	post-teen pop	56.825509	0.635626	0.716008	-5.540277	0.082358	0.153024	0.009367	0.180314	0.555087	123.850051	208598.733392
15	permanent wave	54.000905	0.530724	0.709683	-7.580004	0.050507	0.144509	0.087302	0.189590	0.545103	124.876413	244210.825339
9	hip pop	53.844745	0.675424	0.621870	-6.871198	0.122393	0.255173	0.031629	0.172780	0.514428	116.026076	211897.167994
8	hip hop	53.773071	0.719628	0.565940	-8.243336	0.189124	0.308059	0.218851	0.173616	0.509257	118.260575	181696.042360
19	reggaeton	52.869336	0.760954	0.746515	-5.336615	0.123065	0.201285	0.003761	0.182066	0.678986	119.256106	218115.869336
3	dance pop	52.079353	0.655752	0.742189	-5.768586	0.075837	0.144161	0.048890	0.176795	0.505211	120.106639	207832.938367
12	latin pop	51.099842	0.686111	0.689050	-6.186886	0.090443	0.247439	0.014786	0.188604	0.607369	119.638224	216682.389065
23	urban contemporary	50.523843	0.651922	0.572769	-7.625293	0.130267	0.298932	0.023077	0.172841	0.470657	118.260871	228450.264057
21	trap	50.308288	0.715405	0.655576	-6.528663	0.144863	0.216218	0.067978	0.166972	0.437307	130.034411	200910.660728
16	pop edm	45.686223	0.647744	0.742543	-5.453845	0.085093	0.136459	0.047935	0.196825	0.464772	123.169141	205710.918260
11	latin hip hop	43.451087	0.723135	0.726298	-6.195614	0.123441	0.152912	0.043954	0.176899	0.618276	119.127287	225658.317029
22	tropical	43.327640	0.692133	0.675914	-7.112600	0.072849	0.256820	0.104120	0.176538	0.533140	116.510839	204810.373447
5	electropop	42.725142	0.638609	0.723269	-6.567401	0.069747	0.134555	0.100840	0.182373	0.512342	122.357326	235876.772017
10	indie poptimism	42.475478	0.629596	0.640230	-7.050846	0.070483	0.233985	0.068015	0.169848	0.459962	117.780169	216423.044856
2	classic rock	40.809414	0.545396	0.699240	-8.287437	0.052463	0.191351	0.050040	0.191167	0.609958	123.612147	256666.654321
0	album rock	38.322066	0.525020	0.664189	-8.888486	0.051450	0.205905	0.075451	0.222909	0.520844	122.464300	255363.044131
20	southern hip hop	36.445970	0.714681	0.680922	-6.908566	0.201511	0.117409	0.022481	0.209483	0.554183	119.118353	247029.002985
7	hard rock	35.841077	0.488084	0.828541	-6.053844	0.072091	0.061864	0.045356	0.209477	0.480058	128.084324	239897.417508
4	electro house	35.510258	0.701628	0.800044	-5.842447	0.093483	0.092875	0.321228	0.192536	0.428701	124.976406	216682.578425
6	gangster rap	35.139232	0.724025	0.688549	-6.561617	0.247118	0.152902	0.015051	0.209384	0.504932	116.285976	217581.821674
13	neo soul	32.687233	0.645015	0.541685	-8.332789	0.122204	0.314412	0.041362	0.177927	0.510043	110.101762	239197.748931
1	big room	32.282753	0.619551	0.860316	-4.703041	0.093293	0.042411	0.238905	0.251372	0.324091	128.872881	203852.392206
14	new jack swing	28.032657	0.723365	0.650324	-8.587335	0.086053	0.137996	0.015188	0.177191	0.655586	113.167402	275128.552515
18	progressive electro house	26.867883	0.645908	0.816206	-5.541605	0.077971	0.051983	0.262385	0.214263	0.374506	126.538718	254006.402985

Teen pop is the most popular subgenre playlist.

spotify\
    .groupby(["playlist_subgenre"])["track_popularity"]\
    .mean().reset_index().sort_values("track_popularity", ascending=False)

	playlist_subgenre	track_popularity
17	post-teen pop	56.825509
15	permanent wave	54.000905
9	hip pop	53.844745
8	hip hop	53.773071
19	reggaeton	52.869336
3	dance pop	52.079353
12	latin pop	51.099842
23	urban contemporary	50.523843
21	trap	50.308288
16	pop edm	45.686223
11	latin hip hop	43.451087
22	tropical	43.327640
5	electropop	42.725142
10	indie poptimism	42.475478
2	classic rock	40.809414
0	album rock	38.322066
20	southern hip hop	36.445970
7	hard rock	35.841077
4	electro house	35.510258
6	gangster rap	35.139232
13	neo soul	32.687233
1	big room	32.282753
14	new jack swing	28.032657
18	progressive electro house	26.867883

Duplicated data

In this section, only the code will be done to remove duplicated rows from the dataset. This will ensure that the analysis and results are more reliable.

spotify = spotify.loc[~spotify.track_id.duplicated(), :]

Clustering: Revisited

In this iteration of the clustering exercise, we will apply hierarchial clustering.

cluster_vars = [
    "danceability", "energy", "loudness", "speechiness",
    "acousticness", "instrumentalness", "liveness", "valence",
    "tempo", "duration_ms"
]

spotify_cluster = spotify.dropna(subset=cluster_vars + ["track_popularity"]).copy()

X_cluster = spotify_cluster[cluster_vars].values

X_scaled = StandardScaler().fit_transform(X_cluster)

inertias = []
ks = list(range(1,20))
for k in ks:
    km = KMeans(n_clusters=k, n_init=10, random_state=0)
    km.fit(X_scaled)
    inertias.append(km.inertia_)

plt.figure(figsize=(6, 4))
plt.plot(ks, inertias, marker="o")
plt.xlabel("Number of clusters (k)")
plt.ylabel("Inertia (within-cluster SSE)")
plt.title("Elbow plot for k-means clustering")
plt.tight_layout()
plt.show()

We will try hierarchial clustering.

from scipy.cluster import hierarchy

hclust_ward = hierarchy.ward(X_scaled)

fig = plt.figure(figsize=(12, 7))
dn = hierarchy.dendrogram(hclust_ward, no_labels=True)
plt.show()

It seems that we have 6 distinct clusters.

spotify['k'] = pd.Series(hierarchy.cut_tree(hclust_ward, n_clusters=4).ravel(),index = spotify.index).astype('category')

sns.catplot(data = spotify , x="k", y="track_popularity", kind="box", aspect=1)
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

spotify.groupby('k')[continuous_vars + ['track_popularity']].mean()

	danceability	energy	loudness	speechiness	acousticness	instrumentalness	liveness	valence	tempo	duration_ms	track_popularity
k
0	0.652164	0.736680	-6.260000	0.076657	0.123858	0.021978	0.207172	0.542251	121.422971	226445.501476	39.903129
1	0.709523	0.675679	-6.743498	0.294719	0.154332	0.006747	0.175967	0.529467	121.869349	219106.025151	39.818913
2	0.657353	0.718471	-7.829748	0.077385	0.162057	0.712202	0.159662	0.400815	122.983098	231470.241071	31.884615
3	0.578474	0.457930	-9.547663	0.083113	0.575174	0.025900	0.137563	0.386748	114.525539	232882.608113	42.522751

sns.catplot(data = spotify , x= 'k' , kind = 'count', aspect=1)
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

sns.catplot(data = spotify , x= 'k' , kind = 'count', aspect=1, hue='playlist_genre')
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

sns.catplot(data = spotify , y= 'k' , kind = 'count', aspect=1, hue='release_year')
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

spotify.groupby('k')[continuous_vars + ['track_popularity','playlist_genre']].count()

	danceability	energy	loudness	speechiness	acousticness	instrumentalness	liveness	valence	tempo	duration_ms	track_popularity	playlist_genre
k
0	18633	18633	18633	18633	18633	18633	18633	18633	18633	18633	18633	18633
1	3976	3976	3976	3976	3976	3976	3976	3976	3976	3976	3976	3976
2	2912	2912	2912	2912	2912	2912	2912	2912	2912	2912	2912	2912
3	2835	2835	2835	2835	2835	2835	2835	2835	2835	2835	2835	2835

pd.crosstab(spotify['k'], spotify['playlist_genre'])

playlist_genre	edm	latin	pop	r&b	rap	rock
k
0	3087	3090	3873	2714	2446	3423
1	295	459	305	738	2130	49
2	1393	234	371	122	500	292
3	102	354	583	930	325	541

spotify.groupby('k')[continuous_vars + ['track_popularity']].mean()

	danceability	energy	loudness	speechiness	acousticness	instrumentalness	liveness	valence	tempo	duration_ms	track_popularity
k
0	0.652164	0.736680	-6.260000	0.076657	0.123858	0.021978	0.207172	0.542251	121.422971	226445.501476	39.903129
1	0.709523	0.675679	-6.743498	0.294719	0.154332	0.006747	0.175967	0.529467	121.869349	219106.025151	39.818913
2	0.657353	0.718471	-7.829748	0.077385	0.162057	0.712202	0.159662	0.400815	122.983098	231470.241071	31.884615
3	0.578474	0.457930	-9.547663	0.083113	0.575174	0.025900	0.137563	0.386748	114.525539	232882.608113	42.522751

Modeling

There are some variables that we want to create specifically for modelling.

def my_coefplot(mod, figsize_use=(10, 4)):
    fig, ax = plt.subplots(figsize=figsize_use)
    
    ax.errorbar( y=mod.params.index,
                 x=mod.params,
                 xerr = 2 * mod.bse,
                 fmt='o', color='k', ecolor='k', elinewidth=2, ms=10)
    
    ax.axvline(x=0, linestyle='--', linewidth=3.5, color='grey')
    
    ax.set_xlabel('coefficient value')
    
    plt.show()

spotify.info()

<class 'pandas.core.frame.DataFrame'>
Index: 28356 entries, 0 to 32832
Data columns (total 26 columns):
 #   Column                    Non-Null Count  Dtype         
---  ------                    --------------  -----         
 0   track_id                  28356 non-null  object        
 1   track_name                28352 non-null  object        
 2   track_artist              28352 non-null  object        
 3   track_popularity          28356 non-null  int64         
 4   track_album_id            28356 non-null  object        
 5   track_album_name          28352 non-null  object        
 6   track_album_release_date  26675 non-null  datetime64[ns]
 7   playlist_name             28356 non-null  object        
 8   playlist_id               28356 non-null  object        
 9   playlist_genre            28356 non-null  object        
 10  playlist_subgenre         28356 non-null  object        
 11  danceability              28356 non-null  float64       
 12  energy                    28356 non-null  float64       
 13  key                       28356 non-null  int64         
 14  loudness                  28356 non-null  float64       
 15  mode                      28356 non-null  int64         
 16  speechiness               28356 non-null  float64       
 17  acousticness              28356 non-null  float64       
 18  instrumentalness          28356 non-null  float64       
 19  liveness                  28356 non-null  float64       
 20  valence                   28356 non-null  float64       
 21  tempo                     28356 non-null  float64       
 22  duration_ms               28356 non-null  int64         
 23  release_year              26675 non-null  float64       
 24  release_month             26675 non-null  float64       
 25  k                         28356 non-null  category      
dtypes: category(1), datetime64[ns](1), float64(11), int64(4), object(9)
memory usage: 5.7+ MB

spotify_model = spotify.copy()

artist_vars = spotify.groupby(['track_artist']).agg(
    artist_avg_popularity=('track_popularity','mean'),
    artist_n_tracks=('track_popularity','count'),
    artist_n_genres=('playlist_genre','nunique'),
    artist_n_playlists=('playlist_id','nunique'),
    artist_n_subgenres=('playlist_subgenre','nunique'),
    artist_hit_rate=('track_popularity', lambda x: np.where(x > 70,1,0).mean()),
    artist_energy_mean=('energy','mean'),
    artist_danceability_mean=('danceability','mean'),
    artist_valence_mean=('valence','mean'),
    artist_tempo_mean=('tempo','mean'),
    artist_acousticness_mean=('acousticness','mean'),
    artist_speechiness_mean=('speechiness','mean'),
    artist_instrumentalness_mean=('instrumentalness','mean'),
    artist_liveness_mean=('liveness','mean')
).reset_index().sort_values(by='artist_n_playlists', ascending=False)

playlist_vars = spotify.groupby(['playlist_id']).agg(
    playlist_avg_popularity=('track_popularity','mean'),
    playlist_n_tracks=('track_popularity','count'),
    playlist_n_genres=('playlist_genre','nunique'),
    playlist_n_subgenres=('playlist_subgenre','nunique')
).reset_index().sort_values(by='playlist_n_tracks', ascending=False)

spotify_model = spotify_model.merge(artist_vars, on='track_artist', how='inner')
spotify_model = spotify_model.merge(playlist_vars, on='playlist_id', how='inner')

def fit_ols(formula, data):
    model = smf.ols(formula=formula, data=data).fit()
    print(model.summary())
    return model

def viz_fitted_vs_actual(fitted, actual, title):
    df_viz = pd.DataFrame({
        'Fitted Values': fitted,
        'Actual Values': actual
    })
    plt.figure(figsize=(6,6))
    sns.scatterplot(data=df_viz, x='Actual Values', y='Fitted Values', alpha=0.3)
    sns.lineplot(data=df_viz, x='Actual Values', y='Actual Values', color='red')
    plt.title(title)
    plt.show()

Are the variables Gaussian ?

spotify_lm = spotify_model.reset_index().rename(columns={'index':'row_id'}).melt(id_vars=categorical_vars, value_vars=continuous_vars+artist_vars.columns.tolist()[1:])

sns.displot( data = spotify_lm , x = 'value', col = 'variable', kind = 'hist', aspect = 2, col_wrap=3, facet_kws={'sharex': False, 'sharey': False}, common_bins=False, kde=True)
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

As is shown by the graph above, the new variable avg_artist_popularity, seems to follow gaussian distribution. The remainin artist related variables will remain as categorical variables. Hence, it is not necessary that are Gaussian like.

However, we will drop artist_n_playlist becasue this kind of information will be already captured essentially in artist_n_genres. Plus, it is easier to work with artist_n_genres since there are only 5 unique values. For the same reason, we will also drop artist_n_subgenre.

We will go ahead and start fitting models.

But first we will first apply natural to some variables and then standardize the values of continious variables.

spotify_model.isna().sum().sort_values(ascending=False)

release_year                    1681
release_month                   1681
track_album_release_date        1681
track_id                           0
artist_n_subgenres                 0
k                                  0
artist_avg_popularity              0
artist_n_tracks                    0
artist_n_genres                    0
artist_n_playlists                 0
artist_hit_rate                    0
tempo                              0
artist_energy_mean                 0
artist_danceability_mean           0
artist_valence_mean                0
artist_tempo_mean                  0
artist_acousticness_mean           0
artist_speechiness_mean            0
artist_instrumentalness_mean       0
duration_ms                        0
valence                            0
track_name                         0
playlist_subgenre                  0
track_artist                       0
track_popularity                   0
track_album_id                     0
track_album_name                   0
playlist_name                      0
playlist_id                        0
playlist_genre                     0
danceability                       0
liveness                           0
energy                             0
key                                0
loudness                           0
mode                               0
speechiness                        0
acousticness                       0
instrumentalness                   0
artist_liveness_mean               0
dtype: int64

cat_var = ['playlist_subgenre', 'mode','artist_n_genres']

cont_var = ['danceability', 'energy','speechiness',
    'acousticness', 'instrumentalness', 'liveness', 'valence',
    'tempo', 'duration_ms', 'artist_avg_popularity',
 'artist_n_tracks',
 'artist_hit_rate',
 'artist_energy_mean',
 'artist_danceability_mean',
 'artist_valence_mean',
 'artist_tempo_mean',
 'artist_acousticness_mean',
 'artist_speechiness_mean',
 'artist_instrumentalness_mean',
 'artist_liveness_mean','playlist_avg_popularity']

cont_features = (
    "danceability + energy  + speechiness + acousticness + instrumentalness + liveness + valence + \
    tempo + duration_ms + artist_avg_popularity + artist_hit_rate + \
    artist_n_tracks + artist_energy_mean + artist_danceability_mean + artist_valence_mean + artist_tempo_mean + \
    artist_acousticness_mean + artist_speechiness_mean + artist_instrumentalness_mean + artist_liveness_mean+ playlist_avg_popularity"
)

cat_features = "playlist_subgenre + mode  + artist_n_genres + key"

'Artist_n_tracks' has more than needed unique values. Therefore, we will group values together to make the modelling work easier to interpret as a categorical variable.

#spotify_model['artist_n_tracks'] = pd.to_numeric(spotify_copy['artist_n_tracks'])
#spotify_model['artist_n_tracks'] = np.where(spotify_copy['artist_n_tracks']<20,'Low',
#                                            np.where(spotify_copy['artist_n_tracks']<40,'Medium','High'))

Natural log of all continious variables.

spotify_model[cont_var] = np.log1p(spotify_model[cont_var])

Now we visualize all continious variables to ensure Gaussian like behaviour.

spotify_lm = spotify_model.reset_index().rename(columns={'index':'row_id'}).melt(id_vars=cat_var, value_vars=cont_var)

sns.displot( data = spotify_lm , x = 'value', col = 'variable', kind = 'hist', aspect = 2, col_wrap=3, facet_kws={'sharex': False, 'sharey': False},kde=True)
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

spotify_model[cat_var] = spotify_model[cat_var].astype('category')

Standardization

x_scaled = pd.DataFrame(StandardScaler().fit_transform(spotify_model[cont_var]), columns=cont_var)

# Fix the typo
spotify_model[cont_var] = pd.DataFrame(
    StandardScaler().fit_transform(spotify_model[cont_var]), 
    columns=cont_var,
    index=spotify_model.index  # Add this line to preserve the index
)

Intercept-only model

f_1 = "track_popularity ~ 1"

m_1 = fit_ols(f_1, spotify_model)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       track_popularity   R-squared:                       0.000
Model:                            OLS   Adj. R-squared:                  0.000
Method:                 Least Squares   F-statistic:                       nan
Date:                Tue, 09 Dec 2025   Prob (F-statistic):                nan
Time:                        17:26:10   Log-Likelihood:            -1.2998e+05
No. Observations:               28352   AIC:                         2.600e+05
Df Residuals:                   28351   BIC:                         2.600e+05
Df Model:                           0                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     39.3353      0.141    279.471      0.000      39.059      39.611
==============================================================================
Omnibus:                     6116.318   Durbin-Watson:                   1.122
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1389.583
Skew:                          -0.232   Prob(JB):                    1.80e-302
Kurtosis:                       2.019   Cond. No.                         1.00
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

my_coefplot(m_1, figsize_use=(8,6))

How many coefficients were estimated?

m_1.params.size

1

How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?

m_1.params[m_1.pvalues < 0.05].size

1

WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?

m_1.params[m_1.pvalues < 0.05]

Intercept    39.33532
dtype: float64

Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values

m1.params[m1.pvalues < 0.05].sort_values(key=abs,ascending=False)

Intercept    39.33532
dtype: float64

Training Performance

print(f'R squared: {m1.rsquared}, RMSE: {m1.mse_resid**0.5}')

R squared: 0.0, RMSE: 23.69944331918895

Observed vs Predicted figure

viz_fitted_vs_actual(m1.fittedvalues, spotify_model['track_popularity'], 'Intercept only Model')

Categorical inputs with additive features

f_2 = "track_popularity ~ +" + cat_features

m_2 = fit_ols(f_2, spotify_model)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       track_popularity   R-squared:                       0.158
Model:                            OLS   Adj. R-squared:                  0.158
Method:                 Least Squares   F-statistic:                     183.9
Date:                Tue, 09 Dec 2025   Prob (F-statistic):               0.00
Time:                        17:26:14   Log-Likelihood:            -1.2753e+05
No. Observations:               28352   AIC:                         2.551e+05
Df Residuals:                   28322   BIC:                         2.554e+05
Df Model:                          29                                         
Covariance Type:            nonrobust                                         
==================================================================================================================
                                                     coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------------------------
Intercept                                         35.3501      0.744     47.503      0.000      33.892      36.809
playlist_subgenre[T.big room]                     -8.9385      0.960     -9.315      0.000     -10.819      -7.058
playlist_subgenre[T.classic rock]                  0.1173      0.941      0.125      0.901      -1.728       1.962
playlist_subgenre[T.dance pop]                    12.2696      0.912     13.461      0.000      10.483      14.056
playlist_subgenre[T.electro house]                -3.2797      0.891     -3.679      0.000      -5.027      -1.533
playlist_subgenre[T.electropop]                   -0.7196      0.919     -0.783      0.434      -2.521       1.082
playlist_subgenre[T.gangster rap]                 -4.7416      0.906     -5.236      0.000      -6.517      -2.967
playlist_subgenre[T.hard rock]                    -3.3554      0.923     -3.636      0.000      -5.164      -1.547
playlist_subgenre[T.hip hop]                      15.8711      0.909     17.466      0.000      14.090      17.652
playlist_subgenre[T.hip pop]                       6.4456      1.025      6.290      0.000       4.437       8.454
playlist_subgenre[T.indie poptimism]               2.4823      0.874      2.842      0.004       0.770       4.194
playlist_subgenre[T.latin hip hop]                -5.2220      0.928     -5.629      0.000      -7.040      -3.404
playlist_subgenre[T.latin pop]                     9.4415      0.942     10.020      0.000       7.595      11.288
playlist_subgenre[T.neo soul]                     -6.7874      0.885     -7.671      0.000      -8.522      -5.053
playlist_subgenre[T.new jack swing]              -11.6645      0.958    -12.175      0.000     -13.542      -9.787
playlist_subgenre[T.permanent wave]               13.9897      0.973     14.380      0.000      12.083      15.897
playlist_subgenre[T.pop edm]                      -2.9426      0.979     -3.007      0.003      -4.861      -1.024
playlist_subgenre[T.post-teen pop]                14.5635      0.963     15.121      0.000      12.676      16.451
playlist_subgenre[T.progressive electro house]   -14.0040      0.887    -15.794      0.000     -15.742     -12.266
playlist_subgenre[T.reggaeton]                     7.0243      1.074      6.541      0.000       4.919       9.129
playlist_subgenre[T.southern hip hop]             -2.8892      0.870     -3.320      0.001      -4.595      -1.183
playlist_subgenre[T.trap]                         10.8537      0.924     11.744      0.000       9.042      12.665
playlist_subgenre[T.tropical]                      4.0332      0.932      4.329      0.000       2.207       5.859
playlist_subgenre[T.urban contemporary]            7.9415      0.928      8.560      0.000       6.123       9.760
mode[T.1]                                          0.0280      0.268      0.104      0.917      -0.497       0.553
artist_n_genres[T.2]                               5.3978      0.327     16.497      0.000       4.757       6.039
artist_n_genres[T.3]                               8.9565      0.449     19.947      0.000       8.076       9.837
artist_n_genres[T.4]                              11.4734      0.596     19.265      0.000      10.306      12.641
artist_n_genres[T.5]                               5.3364      1.064      5.013      0.000       3.250       7.423
key                                               -0.0050      0.036     -0.137      0.891      -0.076       0.066
==============================================================================
Omnibus:                     1833.362   Durbin-Watson:                   1.296
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1266.200
Skew:                          -0.408   Prob(JB):                    1.12e-275
Kurtosis:                       2.363   Cond. No.                         171.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

my_coefplot(m_2, figsize_use=(8,12))

How many coefficients were estimated?

m_2.params.size

30

How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?

print(m_2.params[m_2.pvalues < 0.05].size)

26

WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?

m_2.params[m_2.pvalues < 0.05]

Intercept                                         35.350127
playlist_subgenre[T.big room]                     -8.938483
playlist_subgenre[T.dance pop]                    12.269645
playlist_subgenre[T.electro house]                -3.279704
playlist_subgenre[T.gangster rap]                 -4.741553
playlist_subgenre[T.hard rock]                    -3.355361
playlist_subgenre[T.hip hop]                      15.871143
playlist_subgenre[T.hip pop]                       6.445567
playlist_subgenre[T.indie poptimism]               2.482334
playlist_subgenre[T.latin hip hop]                -5.222045
playlist_subgenre[T.latin pop]                     9.441476
playlist_subgenre[T.neo soul]                     -6.787420
playlist_subgenre[T.new jack swing]              -11.664472
playlist_subgenre[T.permanent wave]               13.989716
playlist_subgenre[T.pop edm]                      -2.942566
playlist_subgenre[T.post-teen pop]                14.563470
playlist_subgenre[T.progressive electro house]   -14.004006
playlist_subgenre[T.reggaeton]                     7.024311
playlist_subgenre[T.southern hip hop]             -2.889238
playlist_subgenre[T.trap]                         10.853732
playlist_subgenre[T.tropical]                      4.033236
playlist_subgenre[T.urban contemporary]            7.941489
artist_n_genres[T.2]                               5.397848
artist_n_genres[T.3]                               8.956454
artist_n_genres[T.4]                              11.473385
artist_n_genres[T.5]                               5.336372
dtype: float64

Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?

print(m_2.params[m_2.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3])

playlist_subgenre[T.hip hop]          15.871143
playlist_subgenre[T.post-teen pop]    14.563470
dtype: float64

Show the predicted vs observed figure for the training set, and the R-squared and RMSE on the training set.

def viz_fitted_vs_actual(fitted, actual, title):
    df_viz = pd.DataFrame({
        'Fitted Values': fitted,
        'Actual Values': actual
    })
    plt.figure(figsize=(6,6))
    sns.scatterplot(data=df_viz, x='Actual Values', y='Fitted Values', alpha=0.3)
    sns.lineplot(data=df_viz, x='Actual Values', y='Actual Values', color='red')
    plt.title(title)
    plt.show()

viz_fitted_vs_actual(m_2.fittedvalues, spotify_model['track_popularity'],'Categorical only Model')

Training performance

print(f'R squared: {m_cat.rsquared}, RMSE: {m_cat.mse_resid**0.5}')

R squared: 0.15849282400371167, RMSE: 21.75150385497045

Categorical only model barely does better than the intercept only model as indicated by RMSE of 21 vs 23.

Continuous inputs with linear additive features

f_3 = "track_popularity ~ " + cont_features

m_3 = fit_ols(f_3, spotify_model)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       track_popularity   R-squared:                       0.528
Model:                            OLS   Adj. R-squared:                  0.527
Method:                 Least Squares   F-statistic:                     1507.
Date:                Wed, 10 Dec 2025   Prob (F-statistic):               0.00
Time:                        03:46:45   Log-Likelihood:            -1.1934e+05
No. Observations:               28352   AIC:                         2.387e+05
Df Residuals:                   28330   BIC:                         2.389e+05
Df Model:                          21                                         
Covariance Type:            nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
Intercept                       39.3353      0.097    406.485      0.000      39.146      39.525
danceability                     0.6810      0.183      3.725      0.000       0.323       1.039
energy                          -1.1725      0.199     -5.883      0.000      -1.563      -0.782
speechiness                     -0.2949      0.170     -1.734      0.083      -0.628       0.038
acousticness                     0.1728      0.182      0.951      0.341      -0.183       0.529
instrumentalness                -1.0286      0.191     -5.380      0.000      -1.403      -0.654
liveness                        -0.2052      0.130     -1.577      0.115      -0.460       0.050
valence                          0.4998      0.175      2.857      0.004       0.157       0.843
tempo                            0.1822      0.136      1.344      0.179      -0.084       0.448
duration_ms                      0.0120      0.101      0.118      0.906      -0.186       0.210
artist_avg_popularity            9.9201      0.116     85.453      0.000       9.693      10.148
artist_hit_rate                  3.7516      0.109     34.514      0.000       3.539       3.965
artist_n_tracks                 -0.8198      0.105     -7.803      0.000      -1.026      -0.614
artist_energy_mean               0.8152      0.212      3.844      0.000       0.399       1.231
artist_danceability_mean        -0.5015      0.188     -2.672      0.008      -0.869      -0.134
artist_valence_mean             -0.1989      0.177     -1.126      0.260      -0.545       0.147
artist_tempo_mean               -0.0279      0.137     -0.204      0.839      -0.297       0.241
artist_acousticness_mean        -0.2629      0.195     -1.346      0.178      -0.646       0.120
artist_speechiness_mean          0.2223      0.174      1.279      0.201      -0.118       0.563
artist_instrumentalness_mean     1.1505      0.195      5.913      0.000       0.769       1.532
artist_liveness_mean             0.0987      0.133      0.744      0.457      -0.161       0.359
playlist_avg_popularity          8.0040      0.118     67.683      0.000       7.772       8.236
==============================================================================
Omnibus:                     1996.522   Durbin-Watson:                   1.559
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2555.827
Skew:                          -0.650   Prob(JB):                         0.00
Kurtosis:                       3.688   Cond. No.                         6.40
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

my_coefplot(m_3)

i. How many coefficients were estimated?

10 Coefficients were estimated.

ii. How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds? Nearly all coefficients are statsitically significant except for mode.

iii. WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features? iv. Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?

How many coefficients were estimated?

m_3.params.size

22

How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?

m_3.params[m_3.pvalues < 0.05].size

12

WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?

m_3.params[m_3.pvalues < 0.05]

Intercept                       39.335320
danceability                     0.681033
energy                          -1.172547
instrumentalness                -1.028642
valence                          0.499804
artist_avg_popularity            9.920143
artist_hit_rate                  3.751601
artist_n_tracks                 -0.819824
artist_energy_mean               0.815204
artist_danceability_mean        -0.501500
artist_instrumentalness_mean     1.150451
playlist_avg_popularity          8.003964
dtype: float64

Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?

m_3.params[m_3.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3]

artist_avg_popularity    13.358650
artist_hit_rate           5.209513
dtype: float64

For each model show the predicted vs observed figure for the training set, and the R-squared and RMSE on the training set.

print(f'R squared: {m_3.rsquared}, RMSE: {m_3.mse_resid**0.5}')

R squared: 0.5276510268815217, RMSE: 16.294105968324935

viz_fitted_vs_actual(m_3.fittedvalues, spotify_model['track_popularity'], 'Continuous only Model')

All inputs (continuous + categorical) additive

f_4 = (
    "track_popularity ~ " + cont_features + " + " + cat_features
)

m_4 = fit_ols(f_4, spotify_model)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       track_popularity   R-squared:                       0.533
Model:                            OLS   Adj. R-squared:                  0.533
Method:                 Least Squares   F-statistic:                     688.5
Date:                Wed, 10 Dec 2025   Prob (F-statistic):               0.00
Time:                        03:49:48   Log-Likelihood:            -1.1917e+05
No. Observations:               28352   AIC:                         2.384e+05
Df Residuals:                   28304   BIC:                         2.388e+05
Df Model:                          47                                         
Covariance Type:            nonrobust                                         
==================================================================================================================
                                                     coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------------------------
Intercept                                         42.1861      0.599     70.481      0.000      41.013      43.359
playlist_subgenre[T.big room]                     -3.0296      0.785     -3.860      0.000      -4.568      -1.491
playlist_subgenre[T.classic rock]                 -2.9838      0.706     -4.226      0.000      -4.368      -1.600
playlist_subgenre[T.dance pop]                     1.7435      0.717      2.430      0.015       0.337       3.150
playlist_subgenre[T.electro house]                -2.4618      0.736     -3.345      0.001      -3.904      -1.019
playlist_subgenre[T.electropop]                   -0.5550      0.707     -0.785      0.433      -1.941       0.831
playlist_subgenre[T.gangster rap]                 -4.3557      0.759     -5.739      0.000      -5.843      -2.868
playlist_subgenre[T.hard rock]                    -4.1508      0.711     -5.836      0.000      -5.545      -2.757
playlist_subgenre[T.hip hop]                       0.3768      0.760      0.496      0.620      -1.112       1.866
playlist_subgenre[T.hip pop]                      -0.6393      0.800     -0.799      0.424      -2.208       0.929
playlist_subgenre[T.indie poptimism]              -1.4229      0.679     -2.096      0.036      -2.754      -0.092
playlist_subgenre[T.latin hip hop]                 0.7046      0.737      0.956      0.339      -0.740       2.149
playlist_subgenre[T.latin pop]                    -1.5018      0.734     -2.046      0.041      -2.940      -0.063
playlist_subgenre[T.neo soul]                     -1.1221      0.694     -1.618      0.106      -2.482       0.237
playlist_subgenre[T.new jack swing]               -4.7197      0.748     -6.306      0.000      -6.187      -3.253
playlist_subgenre[T.permanent wave]                1.0189      0.740      1.377      0.169      -0.432       2.470
playlist_subgenre[T.pop edm]                      -3.3656      0.765     -4.399      0.000      -4.865      -1.866
playlist_subgenre[T.post-teen pop]                 2.5951      0.746      3.477      0.001       1.132       4.058
playlist_subgenre[T.progressive electro house]    -0.9300      0.728     -1.277      0.202      -2.358       0.498
playlist_subgenre[T.reggaeton]                    -2.1048      0.842     -2.501      0.012      -3.754      -0.455
playlist_subgenre[T.southern hip hop]             -3.6225      0.708     -5.114      0.000      -5.011      -2.234
playlist_subgenre[T.trap]                         -1.8376      0.749     -2.452      0.014      -3.306      -0.369
playlist_subgenre[T.tropical]                     -2.3484      0.737     -3.186      0.001      -3.793      -0.904
playlist_subgenre[T.urban contemporary]           -0.2052      0.725     -0.283      0.777      -1.625       1.215
danceability                                       0.6975      0.182      3.834      0.000       0.341       1.054
energy                                            -1.0954      0.199     -5.516      0.000      -1.485      -0.706
speechiness                                       -0.2468      0.169     -1.459      0.145      -0.578       0.085
acousticness                                       0.1571      0.181      0.869      0.385      -0.197       0.511
instrumentalness                                  -0.9825      0.190     -5.158      0.000      -1.356      -0.609
liveness                                          -0.1880      0.129     -1.453      0.146      -0.442       0.066
valence                                            0.4461      0.174      2.559      0.011       0.104       0.788
tempo                                              0.1757      0.135      1.302      0.193      -0.089       0.440
duration_ms                                        0.0989      0.105      0.939      0.348      -0.108       0.305
artist_avg_popularity                             10.0953      0.117     86.537      0.000       9.867      10.324
artist_hit_rate                                    3.7024      0.115     32.276      0.000       3.478       3.927
artist_n_tracks                                   -0.2432      0.134     -1.813      0.070      -0.506       0.020
artist_energy_mean                                 0.8602      0.217      3.967      0.000       0.435       1.285
artist_danceability_mean                          -0.3533      0.199     -1.774      0.076      -0.744       0.037
artist_valence_mean                               -0.3473      0.182     -1.906      0.057      -0.705       0.010
artist_tempo_mean                                 -0.0310      0.137     -0.226      0.822      -0.300       0.238
artist_acousticness_mean                          -0.3456      0.197     -1.756      0.079      -0.731       0.040
artist_speechiness_mean                            0.4145      0.185      2.240      0.025       0.052       0.777
artist_instrumentalness_mean                       0.9694      0.198      4.905      0.000       0.582       1.357
artist_liveness_mean                               0.1215      0.132      0.918      0.359      -0.138       0.381
playlist_avg_popularity                            7.5881      0.130     58.155      0.000       7.332       7.844
mode                                               0.1186      0.200      0.593      0.553      -0.273       0.510
artist_n_genres                                   -0.9449      0.143     -6.618      0.000      -1.225      -0.665
key                                                0.0200      0.027      0.737      0.461      -0.033       0.073
==============================================================================
Omnibus:                     1978.851   Durbin-Watson:                   1.576
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2524.834
Skew:                          -0.648   Prob(JB):                         0.00
Kurtosis:                       3.677   Cond. No.                         187.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

my_coefplot(m_all, figsize_use=(10,12))

How many coefficients were estimated?

m_4.params.size

48

How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?

m_4.params[m_4.pvalues < 0.05].size

27

WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?

m_4.params[m_4.pvalues < 0.05]

Intercept                                42.186147
playlist_subgenre[T.big room]            -3.029620
playlist_subgenre[T.classic rock]        -2.983779
playlist_subgenre[T.dance pop]            1.743533
playlist_subgenre[T.electro house]       -2.461842
playlist_subgenre[T.gangster rap]        -4.355652
playlist_subgenre[T.hard rock]           -4.150836
playlist_subgenre[T.indie poptimism]     -1.422858
playlist_subgenre[T.latin pop]           -1.501753
playlist_subgenre[T.new jack swing]      -4.719727
playlist_subgenre[T.pop edm]             -3.365604
playlist_subgenre[T.post-teen pop]        2.595075
playlist_subgenre[T.reggaeton]           -2.104822
playlist_subgenre[T.southern hip hop]    -3.622466
playlist_subgenre[T.trap]                -1.837599
playlist_subgenre[T.tropical]            -2.348388
danceability                              0.697492
energy                                   -1.095441
instrumentalness                         -0.982516
valence                                   0.446091
artist_avg_popularity                    10.095314
artist_hit_rate                           3.702357
artist_energy_mean                        0.860172
artist_speechiness_mean                   0.414505
artist_instrumentalness_mean              0.969382
playlist_avg_popularity                   7.588078
artist_n_genres                          -0.944934
dtype: float64

Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?

m_4.params[m_4.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3]

artist_avg_popularity      10.095314
playlist_avg_popularity     7.588078
dtype: float64

Training Performance

print(f'R squared: {m_4.rsquared}, RMSE: {m_4.mse_resid**0.5}')

R squared: 0.5334176551680413, RMSE: 16.20177433293829

The performance is certianly better than average as shown by the higher r squared and lower rmse. However, it is only bit better than continuous terms only.

Continuous inputs with linear main effect and pair-wise interactions.

f_5 =  "track_popularity ~ (danceability + energy  + speechiness + acousticness + instrumentalness + liveness + valence + tempo + duration_ms \
    + artist_avg_popularity + artist_hit_rate + artist_n_tracks + playlist_avg_popularity )**2"

m_5 = fit_ols(f_5, spotify_model)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       track_popularity   R-squared:                       0.582
Model:                            OLS   Adj. R-squared:                  0.581
Method:                 Least Squares   F-statistic:                     432.2
Date:                Wed, 10 Dec 2025   Prob (F-statistic):               0.00
Time:                        03:50:58   Log-Likelihood:            -1.1761e+05
No. Observations:               28352   AIC:                         2.354e+05
Df Residuals:                   28260   BIC:                         2.362e+05
Df Model:                          91                                         
Covariance Type:            nonrobust                                         
=================================================================================================================
                                                    coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------------------------------
Intercept                                        35.5263      0.185    192.019      0.000      35.164      35.889
danceability                                      0.0442      0.110      0.401      0.689      -0.172       0.261
energy                                           -0.4793      0.126     -3.792      0.000      -0.727      -0.232
speechiness                                      -0.0622      0.105     -0.593      0.553      -0.268       0.143
acousticness                                     -0.0199      0.127     -0.157      0.876      -0.269       0.229
instrumentalness                                  0.0408      0.141      0.289      0.773      -0.236       0.318
liveness                                         -0.0995      0.100     -0.997      0.319      -0.295       0.096
valence                                           0.2222      0.107      2.084      0.037       0.013       0.431
tempo                                             0.1154      0.114      1.016      0.310      -0.107       0.338
duration_ms                                       0.2685      0.107      2.507      0.012       0.059       0.478
artist_avg_popularity                            17.1344      0.245     69.937      0.000      16.654      17.615
artist_hit_rate                                  -3.2118      0.328     -9.780      0.000      -3.856      -2.568
artist_n_tracks                                   0.2544      0.110      2.310      0.021       0.039       0.470
playlist_avg_popularity                           8.9896      0.123     73.021      0.000       8.748       9.231
danceability:energy                              -0.1635      0.124     -1.321      0.186      -0.406       0.079
danceability:speechiness                          0.1115      0.109      1.022      0.307      -0.102       0.325
danceability:acousticness                         0.2622      0.122      2.146      0.032       0.023       0.502
danceability:instrumentalness                     0.0549      0.105      0.523      0.601      -0.151       0.261
danceability:liveness                             0.2544      0.099      2.574      0.010       0.061       0.448
danceability:valence                              0.0846      0.102      0.829      0.407      -0.115       0.285
danceability:tempo                                0.0201      0.095      0.211      0.833      -0.166       0.206
danceability:duration_ms                          0.0868      0.095      0.913      0.361      -0.100       0.273
danceability:artist_avg_popularity                0.1682      0.127      1.328      0.184      -0.080       0.416
danceability:artist_hit_rate                     -0.2407      0.118     -2.035      0.042      -0.472      -0.009
danceability:artist_n_tracks                      0.2016      0.107      1.876      0.061      -0.009       0.412
danceability:playlist_avg_popularity              0.1502      0.126      1.193      0.233      -0.097       0.397
energy:speechiness                                0.1085      0.118      0.920      0.358      -0.123       0.340
energy:acousticness                              -0.0548      0.092     -0.598      0.550      -0.234       0.125
energy:instrumentalness                          -0.0300      0.109     -0.276      0.782      -0.243       0.183
energy:liveness                                  -0.0846      0.122     -0.693      0.488      -0.324       0.155
energy:valence                                   -0.0815      0.119     -0.682      0.495      -0.316       0.153
energy:tempo                                     -0.0266      0.114     -0.234      0.815      -0.249       0.196
energy:duration_ms                               -0.2561      0.107     -2.388      0.017      -0.466      -0.046
energy:artist_avg_popularity                     -0.2268      0.137     -1.659      0.097      -0.495       0.041
energy:artist_hit_rate                           -0.0689      0.139     -0.497      0.620      -0.341       0.203
energy:artist_n_tracks                           -0.0301      0.128     -0.236      0.814      -0.280       0.220
energy:playlist_avg_popularity                    0.1602      0.149      1.074      0.283      -0.132       0.453
speechiness:acousticness                         -0.0341      0.111     -0.307      0.759      -0.252       0.184
speechiness:instrumentalness                      0.0198      0.139      0.143      0.886      -0.252       0.291
speechiness:liveness                              0.0632      0.091      0.692      0.489      -0.116       0.242
speechiness:valence                              -0.0681      0.110     -0.617      0.537      -0.284       0.148
speechiness:tempo                                 0.0481      0.084      0.574      0.566      -0.116       0.212
speechiness:duration_ms                           0.0514      0.095      0.539      0.590      -0.135       0.238
speechiness:artist_avg_popularity                -0.1873      0.113     -1.664      0.096      -0.408       0.033
speechiness:artist_hit_rate                       0.0086      0.103      0.084      0.933      -0.194       0.211
speechiness:artist_n_tracks                      -0.1645      0.106     -1.559      0.119      -0.371       0.042
speechiness:playlist_avg_popularity               0.1579      0.126      1.257      0.209      -0.088       0.404
acousticness:instrumentalness                     0.1266      0.115      1.098      0.272      -0.099       0.353
acousticness:liveness                             0.0508      0.119      0.425      0.671      -0.183       0.285
acousticness:valence                             -0.1357      0.123     -1.101      0.271      -0.377       0.106
acousticness:tempo                               -0.0122      0.105     -0.116      0.908      -0.218       0.194
acousticness:duration_ms                          0.0462      0.106      0.435      0.663      -0.162       0.254
acousticness:artist_avg_popularity               -0.1642      0.136     -1.211      0.226      -0.430       0.102
acousticness:artist_hit_rate                      0.0098      0.122      0.080      0.936      -0.229       0.248
acousticness:artist_n_tracks                     -0.1795      0.128     -1.407      0.159      -0.429       0.071
acousticness:playlist_avg_popularity             -0.0606      0.148     -0.409      0.683      -0.351       0.230
instrumentalness:liveness                        -0.1387      0.099     -1.399      0.162      -0.333       0.056
instrumentalness:valence                         -0.0059      0.091     -0.064      0.949      -0.184       0.173
instrumentalness:tempo                           -0.0110      0.118     -0.093      0.926      -0.242       0.220
instrumentalness:duration_ms                     -0.0727      0.078     -0.934      0.350      -0.225       0.080
instrumentalness:artist_avg_popularity           -0.1291      0.099     -1.310      0.190      -0.322       0.064
instrumentalness:artist_hit_rate                  0.3146      0.220      1.433      0.152      -0.116       0.745
instrumentalness:artist_n_tracks                  0.0251      0.118      0.212      0.832      -0.207       0.257
instrumentalness:playlist_avg_popularity         -0.1883      0.121     -1.552      0.121      -0.426       0.049
liveness:valence                                 -0.0132      0.106     -0.124      0.901      -0.222       0.195
liveness:tempo                                   -0.0398      0.101     -0.395      0.693      -0.237       0.158
liveness:duration_ms                              0.0909      0.095      0.959      0.338      -0.095       0.277
liveness:artist_avg_popularity                   -0.0716      0.113     -0.633      0.527      -0.293       0.150
liveness:artist_hit_rate                         -0.0180      0.108     -0.168      0.867      -0.229       0.193
liveness:artist_n_tracks                          0.2350      0.098      2.387      0.017       0.042       0.428
liveness:playlist_avg_popularity                 -0.1615      0.109     -1.488      0.137      -0.374       0.051
valence:tempo                                    -0.1527      0.114     -1.344      0.179      -0.375       0.070
valence:duration_ms                              -0.0291      0.098     -0.297      0.767      -0.221       0.163
valence:artist_avg_popularity                    -0.1838      0.116     -1.583      0.113      -0.411       0.044
valence:artist_hit_rate                           0.1598      0.124      1.293      0.196      -0.082       0.402
valence:artist_n_tracks                          -0.1879      0.112     -1.683      0.092      -0.407       0.031
valence:playlist_avg_popularity                   0.1540      0.124      1.246      0.213      -0.088       0.396
tempo:duration_ms                                 0.0027      0.058      0.046      0.964      -0.111       0.117
tempo:artist_avg_popularity                       0.2137      0.117      1.832      0.067      -0.015       0.442
tempo:artist_hit_rate                            -0.0594      0.101     -0.589      0.556      -0.257       0.138
tempo:artist_n_tracks                             0.0805      0.104      0.772      0.440      -0.124       0.285
tempo:playlist_avg_popularity                    -0.2858      0.123     -2.315      0.021      -0.528      -0.044
duration_ms:artist_avg_popularity                -0.0373      0.107     -0.349      0.727      -0.247       0.172
duration_ms:artist_hit_rate                      -0.0298      0.125     -0.238      0.812      -0.275       0.216
duration_ms:artist_n_tracks                      -0.2413      0.103     -2.347      0.019      -0.443      -0.040
duration_ms:playlist_avg_popularity               0.1854      0.109      1.703      0.089      -0.028       0.399
artist_avg_popularity:artist_hit_rate             5.9261      0.411     14.417      0.000       5.120       6.732
artist_avg_popularity:artist_n_tracks             0.9351      0.155      6.016      0.000       0.630       1.240
artist_avg_popularity:playlist_avg_popularity     3.6629      0.081     45.434      0.000       3.505       3.821
artist_hit_rate:artist_n_tracks                  -0.3708      0.129     -2.874      0.004      -0.624      -0.118
artist_hit_rate:playlist_avg_popularity           0.3721      0.154      2.423      0.015       0.071       0.673
artist_n_tracks:playlist_avg_popularity           1.5321      0.117     13.143      0.000       1.304       1.761
==============================================================================
Omnibus:                     1717.612   Durbin-Watson:                   1.706
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2784.162
Skew:                          -0.493   Prob(JB):                         0.00
Kurtosis:                       4.176   Cond. No.                         16.4
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

How many coefficients were estimated?

m_5.params.size

92

How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?

m_5.params[m_5.pvalues < 0.05].size

21

WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?

m_5.params[m_5.pvalues < 0.05]

Intercept                                        35.526294
energy                                           -0.479277
valence                                           0.222200
duration_ms                                       0.268506
artist_avg_popularity                            17.134375
artist_hit_rate                                  -3.211827
artist_n_tracks                                   0.254364
playlist_avg_popularity                           8.989586
danceability:acousticness                         0.262206
danceability:liveness                             0.254387
danceability:artist_hit_rate                     -0.240670
energy:duration_ms                               -0.256102
liveness:artist_n_tracks                          0.235014
tempo:playlist_avg_popularity                    -0.285812
duration_ms:artist_n_tracks                      -0.241334
artist_avg_popularity:artist_hit_rate             5.926103
artist_avg_popularity:artist_n_tracks             0.935135
artist_avg_popularity:playlist_avg_popularity     3.662950
artist_hit_rate:artist_n_tracks                  -0.370850
artist_hit_rate:playlist_avg_popularity           0.372104
artist_n_tracks:playlist_avg_popularity           1.532068
dtype: float64

Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?

m_5.params[m_5.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3]

artist_avg_popularity      17.134375
playlist_avg_popularity     8.989586
dtype: float64

Training performance

print(f'R squared: {m_5.rsquared}, RMSE: {m_5.mse_resid**0.5}')

R squared: 0.5819117497897595, RMSE: 15.348651962392772

viz_fitted_vs_actual(m_5.fittedvalues, spotify_model['track_popularity'], 'Continuous Model Additive with Interactions')

It is a bit better than the previous model. However, the main insight from this model the most significant features are artist_popularity and playlist_popularity. In addition, interaction between these two features with audio characteristics turned out to be significant as expected. Tracks by popular artists who have have higher hit rate will most likely have more popular tracks on average.

Continuous and Categorical Interaction

f_6 = f"track_popularity ~ artist_avg_popularity*(danceability + energy  + speechiness + acousticness + instrumentalness + liveness + valence +     tempo + duration_ms+ playlist_avg_popularity) + \
        artist_avg_popularity*(artist_hit_rate + artist_n_tracks )+ artist_avg_popularity*({cat_features})+ playlist_avg_popularity*({cat_features})"

Interact the categorical inputs with the continuous inputs. This model must include the linear main effects as well (the formula interface helps with the interactions).

m_6 = fit_ols(f_6, spotify_model)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       track_popularity   R-squared:                       0.586
Model:                            OLS   Adj. R-squared:                  0.584
Method:                 Least Squares   F-statistic:                     387.4
Date:                Wed, 10 Dec 2025   Prob (F-statistic):               0.00
Time:                        03:56:17   Log-Likelihood:            -1.1749e+05
No. Observations:               28352   AIC:                         2.352e+05
Df Residuals:                   28248   BIC:                         2.360e+05
Df Model:                         103                                         
Covariance Type:            nonrobust                                         
==========================================================================================================================================
                                                                             coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------------------------------------------------
Intercept                                                                 37.4800      0.595     62.987      0.000      36.314      38.646
playlist_subgenre[T.big room]                                             -1.1778      0.805     -1.463      0.143      -2.755       0.400
playlist_subgenre[T.classic rock]                                         -0.6759      0.672     -1.006      0.315      -1.993       0.641
playlist_subgenre[T.dance pop]                                            -2.5302      0.874     -2.895      0.004      -4.244      -0.817
playlist_subgenre[T.electro house]                                        -1.4230      0.694     -2.050      0.040      -2.784      -0.062
playlist_subgenre[T.electropop]                                           -1.3680      0.670     -2.041      0.041      -2.682      -0.054
playlist_subgenre[T.gangster rap]                                         -2.4629      0.728     -3.381      0.001      -3.891      -1.035
playlist_subgenre[T.hard rock]                                            -1.6392      0.692     -2.367      0.018      -2.996      -0.282
playlist_subgenre[T.hip hop]                                              -3.2082      1.206     -2.661      0.008      -5.571      -0.845
playlist_subgenre[T.hip pop]                                              -1.6616      0.785     -2.116      0.034      -3.200      -0.123
playlist_subgenre[T.indie poptimism]                                      -1.5530      0.644     -2.410      0.016      -2.816      -0.290
playlist_subgenre[T.latin hip hop]                                        -2.2785      0.708     -3.217      0.001      -3.667      -0.890
playlist_subgenre[T.latin pop]                                            -2.7291      0.755     -3.614      0.000      -4.209      -1.249
playlist_subgenre[T.neo soul]                                             -2.0773      0.687     -3.022      0.003      -3.425      -0.730
playlist_subgenre[T.new jack swing]                                       -1.4588      0.973     -1.499      0.134      -3.367       0.449
playlist_subgenre[T.permanent wave]                                       -2.7360      0.972     -2.815      0.005      -4.641      -0.831
playlist_subgenre[T.pop edm]                                              -2.5417      0.723     -3.514      0.000      -3.959      -1.124
playlist_subgenre[T.post-teen pop]                                         0.3014      0.830      0.363      0.717      -1.326       1.929
playlist_subgenre[T.progressive electro house]                            -1.4377      0.781     -1.841      0.066      -2.968       0.093
playlist_subgenre[T.reggaeton]                                            -3.9607      0.864     -4.582      0.000      -5.655      -2.266
playlist_subgenre[T.southern hip hop]                                     -1.9978      0.661     -3.020      0.003      -3.294      -0.701
playlist_subgenre[T.trap]                                                 -5.1382      0.911     -5.637      0.000      -6.925      -3.352
playlist_subgenre[T.tropical]                                             -3.4184      0.791     -4.320      0.000      -4.969      -1.868
playlist_subgenre[T.urban contemporary]                                   -1.5708      0.731     -2.148      0.032      -3.004      -0.137
artist_avg_popularity                                                     14.8130      0.693     21.372      0.000      13.455      16.172
artist_avg_popularity:playlist_subgenre[T.big room]                        3.9477      0.819      4.819      0.000       2.342       5.553
artist_avg_popularity:playlist_subgenre[T.classic rock]                    2.1470      0.765      2.807      0.005       0.648       3.646
artist_avg_popularity:playlist_subgenre[T.dance pop]                       3.6069      1.017      3.546      0.000       1.613       5.601
artist_avg_popularity:playlist_subgenre[T.electro house]                   2.4778      0.740      3.351      0.001       1.028       3.927
artist_avg_popularity:playlist_subgenre[T.electropop]                      2.1709      0.674      3.219      0.001       0.849       3.493
artist_avg_popularity:playlist_subgenre[T.gangster rap]                    1.6480      0.724      2.278      0.023       0.230       3.066
artist_avg_popularity:playlist_subgenre[T.hard rock]                       4.7148      0.784      6.012      0.000       3.178       6.252
artist_avg_popularity:playlist_subgenre[T.hip hop]                         3.6881      1.176      3.137      0.002       1.383       5.993
artist_avg_popularity:playlist_subgenre[T.hip pop]                         3.3059      0.862      3.836      0.000       1.617       4.995
artist_avg_popularity:playlist_subgenre[T.indie poptimism]                 2.1813      0.678      3.217      0.001       0.852       3.510
artist_avg_popularity:playlist_subgenre[T.latin hip hop]                   1.9882      0.669      2.971      0.003       0.677       3.300
artist_avg_popularity:playlist_subgenre[T.latin pop]                       2.1442      0.820      2.615      0.009       0.537       3.751
artist_avg_popularity:playlist_subgenre[T.neo soul]                        1.4850      0.643      2.309      0.021       0.224       2.746
artist_avg_popularity:playlist_subgenre[T.new jack swing]                  2.9153      0.828      3.521      0.000       1.292       4.538
artist_avg_popularity:playlist_subgenre[T.permanent wave]                  5.0028      1.046      4.781      0.000       2.952       7.054
artist_avg_popularity:playlist_subgenre[T.pop edm]                         0.9624      0.735      1.309      0.191      -0.479       2.403
artist_avg_popularity:playlist_subgenre[T.post-teen pop]                   2.7488      0.894      3.076      0.002       0.997       4.500
artist_avg_popularity:playlist_subgenre[T.progressive electro house]       3.3523      0.657      5.101      0.000       2.064       4.640
artist_avg_popularity:playlist_subgenre[T.reggaeton]                       1.2377      1.159      1.068      0.285      -1.034       3.509
artist_avg_popularity:playlist_subgenre[T.southern hip hop]                2.3091      0.726      3.180      0.001       0.886       3.733
artist_avg_popularity:playlist_subgenre[T.trap]                            3.2798      1.061      3.090      0.002       1.199       5.360
artist_avg_popularity:playlist_subgenre[T.tropical]                        6.4731      0.928      6.977      0.000       4.655       8.291
artist_avg_popularity:playlist_subgenre[T.urban contemporary]              1.3773      0.745      1.848      0.065      -0.084       2.838
danceability                                                               0.3185      0.115      2.762      0.006       0.092       0.545
energy                                                                    -0.3016      0.124     -2.437      0.015      -0.544      -0.059
speechiness                                                                0.0667      0.108      0.619      0.536      -0.145       0.278
acousticness                                                               0.0259      0.115      0.225      0.822      -0.200       0.252
instrumentalness                                                          -0.2796      0.106     -2.631      0.009      -0.488      -0.071
liveness                                                                  -0.1035      0.094     -1.099      0.272      -0.288       0.081
valence                                                                    0.1240      0.111      1.121      0.262      -0.093       0.341
tempo                                                                      0.1202      0.095      1.262      0.207      -0.066       0.307
duration_ms                                                                0.2192      0.103      2.137      0.033       0.018       0.420
playlist_avg_popularity                                                    6.4515      0.602     10.715      0.000       5.271       7.632
playlist_avg_popularity:playlist_subgenre[T.big room]                     -1.1683      0.788     -1.482      0.138      -2.713       0.377
playlist_avg_popularity:playlist_subgenre[T.classic rock]                  3.1587      0.842      3.751      0.000       1.508       4.809
playlist_avg_popularity:playlist_subgenre[T.dance pop]                     2.1412      1.005      2.131      0.033       0.172       4.111
playlist_avg_popularity:playlist_subgenre[T.electro house]                -0.7368      0.679     -1.086      0.278      -2.067       0.593
playlist_avg_popularity:playlist_subgenre[T.electropop]                   -1.8632      0.730     -2.554      0.011      -3.293      -0.433
playlist_avg_popularity:playlist_subgenre[T.gangster rap]                 -0.4371      0.871     -0.502      0.616      -2.144       1.270
playlist_avg_popularity:playlist_subgenre[T.hard rock]                    -0.1524      0.682     -0.224      0.823      -1.489       1.184
playlist_avg_popularity:playlist_subgenre[T.hip hop]                       1.2189      1.366      0.892      0.372      -1.459       3.897
playlist_avg_popularity:playlist_subgenre[T.hip pop]                      -0.7359      0.942     -0.781      0.435      -2.582       1.111
playlist_avg_popularity:playlist_subgenre[T.indie poptimism]               0.7388      0.776      0.952      0.341      -0.782       2.260
playlist_avg_popularity:playlist_subgenre[T.latin hip hop]                -1.8095      0.656     -2.760      0.006      -3.095      -0.524
playlist_avg_popularity:playlist_subgenre[T.latin pop]                     1.3047      0.900      1.450      0.147      -0.459       3.068
playlist_avg_popularity:playlist_subgenre[T.neo soul]                     -0.7222      0.672     -1.074      0.283      -2.040       0.596
playlist_avg_popularity:playlist_subgenre[T.new jack swing]                1.5241      0.981      1.553      0.120      -0.399       3.448
playlist_avg_popularity:playlist_subgenre[T.permanent wave]                2.9793      1.146      2.600      0.009       0.734       5.225
playlist_avg_popularity:playlist_subgenre[T.pop edm]                       0.1174      0.896      0.131      0.896      -1.638       1.873
playlist_avg_popularity:playlist_subgenre[T.post-teen pop]                -0.3376      0.866     -0.390      0.697      -2.035       1.359
playlist_avg_popularity:playlist_subgenre[T.progressive electro house]    -1.7776      0.660     -2.693      0.007      -3.071      -0.484
playlist_avg_popularity:playlist_subgenre[T.reggaeton]                     2.9292      0.927      3.160      0.002       1.112       4.746
playlist_avg_popularity:playlist_subgenre[T.southern hip hop]              1.1845      0.857      1.383      0.167      -0.495       2.864
playlist_avg_popularity:playlist_subgenre[T.trap]                          2.5120      1.144      2.196      0.028       0.270       4.754
playlist_avg_popularity:playlist_subgenre[T.tropical]                      0.0481      1.377      0.035      0.972      -2.651       2.748
playlist_avg_popularity:playlist_subgenre[T.urban contemporary]            0.1396      0.843      0.166      0.868      -1.513       1.792
artist_avg_popularity:danceability                                         0.1957      0.118      1.665      0.096      -0.035       0.426
artist_avg_popularity:energy                                              -0.3158      0.124     -2.544      0.011      -0.559      -0.073
artist_avg_popularity:speechiness                                         -0.1267      0.112     -1.135      0.257      -0.346       0.092
artist_avg_popularity:acousticness                                        -0.0423      0.117     -0.360      0.718      -0.272       0.188
artist_avg_popularity:instrumentalness                                    -0.1551      0.090     -1.715      0.086      -0.332       0.022
artist_avg_popularity:liveness                                            -0.0554      0.093     -0.595      0.552      -0.238       0.127
artist_avg_popularity:valence                                             -0.0317      0.106     -0.299      0.765      -0.240       0.176
artist_avg_popularity:tempo                                                0.0656      0.089      0.735      0.462      -0.109       0.240
artist_avg_popularity:duration_ms                                         -0.0286      0.090     -0.318      0.751      -0.205       0.148
artist_avg_popularity:playlist_avg_popularity                              3.0286      0.102     29.734      0.000       2.829       3.228
artist_hit_rate                                                           -3.3339      0.327    -10.193      0.000      -3.975      -2.693
artist_n_tracks                                                            0.2009      0.130      1.542      0.123      -0.055       0.456
artist_avg_popularity:artist_hit_rate                                      6.0193      0.374     16.097      0.000       5.286       6.752
artist_avg_popularity:artist_n_tracks                                      1.8025      0.147     12.240      0.000       1.514       2.091
mode                                                                       0.1398      0.189      0.740      0.459      -0.230       0.510
artist_n_genres                                                           -0.5382      0.159     -3.382      0.001      -0.850      -0.226
key                                                                        0.0006      0.026      0.025      0.980      -0.050       0.051
artist_avg_popularity:mode                                                -0.3316      0.220     -1.509      0.131      -0.762       0.099
artist_avg_popularity:artist_n_genres                                      0.3579      0.260      1.377      0.168      -0.151       0.867
artist_avg_popularity:key                                                  0.0140      0.030      0.467      0.640      -0.045       0.073
playlist_avg_popularity:mode                                               0.2001      0.218      0.918      0.359      -0.227       0.627
playlist_avg_popularity:artist_n_genres                                    1.5433      0.118     13.127      0.000       1.313       1.774
playlist_avg_popularity:key                                               -0.0018      0.030     -0.061      0.952      -0.060       0.056
==============================================================================
Omnibus:                     1644.834   Durbin-Watson:                   1.715
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2724.593
Skew:                          -0.470   Prob(JB):                         0.00
Kurtosis:                       4.192   Cond. No.                         298.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

my_coefplot(m_6, figsize_use=(12,30))

How many coefficients were estimated?

m_6.params.size

104

How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?

m_6.params[m_6.pvalues < 0.05].size

60

WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?

m_6.params[m_6.pvalues < 0.05].sort_values(key=abs,ascending=False)

Intercept                                                                 37.480028
artist_avg_popularity                                                     14.813024
artist_avg_popularity:playlist_subgenre[T.tropical]                        6.473092
playlist_avg_popularity                                                    6.451494
artist_avg_popularity:artist_hit_rate                                      6.019263
playlist_subgenre[T.trap]                                                 -5.138187
artist_avg_popularity:playlist_subgenre[T.permanent wave]                  5.002814
artist_avg_popularity:playlist_subgenre[T.hard rock]                       4.714800
playlist_subgenre[T.reggaeton]                                            -3.960673
artist_avg_popularity:playlist_subgenre[T.big room]                        3.947721
artist_avg_popularity:playlist_subgenre[T.hip hop]                         3.688101
artist_avg_popularity:playlist_subgenre[T.dance pop]                       3.606861
playlist_subgenre[T.tropical]                                             -3.418394
artist_avg_popularity:playlist_subgenre[T.progressive electro house]       3.352253
artist_hit_rate                                                           -3.333921
artist_avg_popularity:playlist_subgenre[T.hip pop]                         3.305906
artist_avg_popularity:playlist_subgenre[T.trap]                            3.279850
playlist_subgenre[T.hip hop]                                              -3.208179
playlist_avg_popularity:playlist_subgenre[T.classic rock]                  3.158703
artist_avg_popularity:playlist_avg_popularity                              3.028626
playlist_avg_popularity:playlist_subgenre[T.permanent wave]                2.979330
playlist_avg_popularity:playlist_subgenre[T.reggaeton]                     2.929237
artist_avg_popularity:playlist_subgenre[T.new jack swing]                  2.915261
artist_avg_popularity:playlist_subgenre[T.post-teen pop]                   2.748823
playlist_subgenre[T.permanent wave]                                       -2.736028
playlist_subgenre[T.latin pop]                                            -2.729084
playlist_subgenre[T.pop edm]                                              -2.541709
playlist_subgenre[T.dance pop]                                            -2.530190
playlist_avg_popularity:playlist_subgenre[T.trap]                          2.511971
artist_avg_popularity:playlist_subgenre[T.electro house]                   2.477782
playlist_subgenre[T.gangster rap]                                         -2.462878
artist_avg_popularity:playlist_subgenre[T.southern hip hop]                2.309143
playlist_subgenre[T.latin hip hop]                                        -2.278549
artist_avg_popularity:playlist_subgenre[T.indie poptimism]                 2.181290
artist_avg_popularity:playlist_subgenre[T.electropop]                      2.170879
artist_avg_popularity:playlist_subgenre[T.classic rock]                    2.146995
artist_avg_popularity:playlist_subgenre[T.latin pop]                       2.144192
playlist_avg_popularity:playlist_subgenre[T.dance pop]                     2.141230
playlist_subgenre[T.neo soul]                                             -2.077257
playlist_subgenre[T.southern hip hop]                                     -1.997831
artist_avg_popularity:playlist_subgenre[T.latin hip hop]                   1.988158
playlist_avg_popularity:playlist_subgenre[T.electropop]                   -1.863152
playlist_avg_popularity:playlist_subgenre[T.latin hip hop]                -1.809542
artist_avg_popularity:artist_n_tracks                                      1.802462
playlist_avg_popularity:playlist_subgenre[T.progressive electro house]    -1.777596
playlist_subgenre[T.hip pop]                                              -1.661564
artist_avg_popularity:playlist_subgenre[T.gangster rap]                    1.647973
playlist_subgenre[T.hard rock]                                            -1.639171
playlist_subgenre[T.urban contemporary]                                   -1.570840
playlist_subgenre[T.indie poptimism]                                      -1.553003
playlist_avg_popularity:artist_n_genres                                    1.543339
artist_avg_popularity:playlist_subgenre[T.neo soul]                        1.485005
playlist_subgenre[T.electro house]                                        -1.422950
playlist_subgenre[T.electropop]                                           -1.368048
artist_n_genres                                                           -0.538173
danceability                                                               0.318542
artist_avg_popularity:energy                                              -0.315795
energy                                                                    -0.301609
instrumentalness                                                          -0.279625
duration_ms                                                                0.219213
dtype: float64

Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?

m_6.params[m_6.pvalues < 0.05].sort_values(ascending=False)[1:3]

artist_avg_popularity                                  14.813024
artist_avg_popularity:playlist_subgenre[T.tropical]     6.473092
dtype: float64

print(f'R squared: {m_6.rsquared}, RMSE: {m_6.mse_resid**0.5}')

R squared: 0.5855224680078064, RMSE: 15.285476449238704

viz_fitted_vs_actual(m_6.fittedvalues, spotify_model['track_popularity'], 'Final Model with Interactions')

This is the best model so far.

The main insight that is derived is that the interaction between the genres and artist popularity along with characteristic features of a popular song such as danceability, energy, or instrumantelness are significant features of track popularity.

Polynomials

f_7 = "track_popularity ~ \
  (artist_avg_popularity + playlist_avg_popularity + danceability + energy + valence + \
   tempo + duration_ms + artist_hit_rate + artist_n_tracks)*playlist_subgenre + \
  (I(artist_avg_popularity**2) + I(playlist_avg_popularity**2) + I(danceability**2) + I(energy**2) + \
  I(valence**2) + I(tempo**2) + I(duration_ms**2) + \
  I(artist_hit_rate**2) + I(artist_n_tracks**2))*playlist_subgenre"

m_7 = fit_ols(f_7, spotify_model)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       track_popularity   R-squared:                       0.624
Model:                            OLS   Adj. R-squared:                  0.618
Method:                 Least Squares   F-statistic:                     101.7
Date:                Wed, 10 Dec 2025   Prob (F-statistic):               0.00
Time:                        03:59:10   Log-Likelihood:            -1.1611e+05
No. Observations:               28352   AIC:                         2.331e+05
Df Residuals:                   27896   BIC:                         2.369e+05
Df Model:                         455                                         
Covariance Type:            nonrobust                                         
==================================================================================================================================================
                                                                                     coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------------------------------------------------------------
Intercept                                                                         36.2646      1.180     30.732      0.000      33.952      38.578
playlist_subgenre[T.big room]                                                     -1.9686      2.076     -0.948      0.343      -6.038       2.101
playlist_subgenre[T.classic rock]                                                 -4.2232      1.749     -2.415      0.016      -7.651      -0.796
playlist_subgenre[T.dance pop]                                                     1.2536      1.664      0.753      0.451      -2.009       4.516
playlist_subgenre[T.electro house]                                                -1.9996      1.888     -1.059      0.290      -5.701       1.701
playlist_subgenre[T.electropop]                                                   -4.8804      1.563     -3.122      0.002      -7.944      -1.816
playlist_subgenre[T.gangster rap]                                                 -3.2760      1.689     -1.940      0.052      -6.586       0.034
playlist_subgenre[T.hard rock]                                                    -1.1324      1.810     -0.626      0.531      -4.679       2.414
playlist_subgenre[T.hip hop]                                                      -2.3408      2.752     -0.851      0.395      -7.735       3.053
playlist_subgenre[T.hip pop]                                                      -2.6534      1.899     -1.397      0.162      -6.376       1.069
playlist_subgenre[T.indie poptimism]                                              -4.7762      1.517     -3.148      0.002      -7.750      -1.802
playlist_subgenre[T.latin hip hop]                                                -2.5177      1.681     -1.498      0.134      -5.813       0.778
playlist_subgenre[T.latin pop]                                                    -5.9494      1.719     -3.461      0.001      -9.319      -2.580
playlist_subgenre[T.neo soul]                                                     -2.9108      1.597     -1.823      0.068      -6.040       0.219
playlist_subgenre[T.new jack swing]                                                0.0539      2.322      0.023      0.981      -4.498       4.606
playlist_subgenre[T.permanent wave]                                               -3.6638      1.815     -2.018      0.044      -7.222      -0.105
playlist_subgenre[T.pop edm]                                                      -7.8114      1.693     -4.614      0.000     -11.130      -4.493
playlist_subgenre[T.post-teen pop]                                                -3.6794      1.827     -2.014      0.044      -7.261      -0.098
playlist_subgenre[T.progressive electro house]                                    -2.4637      1.824     -1.351      0.177      -6.039       1.111
playlist_subgenre[T.reggaeton]                                                    -5.6652      2.669     -2.122      0.034     -10.897      -0.433
playlist_subgenre[T.southern hip hop]                                             -3.5135      1.655     -2.122      0.034      -6.758      -0.269
playlist_subgenre[T.trap]                                                         -8.4319      1.863     -4.527      0.000     -12.083      -4.781
playlist_subgenre[T.tropical]                                                     -3.5891      1.741     -2.061      0.039      -7.002      -0.176
playlist_subgenre[T.urban contemporary]                                           -4.2484      1.747     -2.432      0.015      -7.672      -0.824
artist_avg_popularity                                                             19.5773      1.165     16.807      0.000      17.294      21.860
artist_avg_popularity:playlist_subgenre[T.big room]                                0.3686      1.760      0.209      0.834      -3.082       3.819
artist_avg_popularity:playlist_subgenre[T.classic rock]                            1.8892      1.609      1.174      0.240      -1.264       5.043
artist_avg_popularity:playlist_subgenre[T.dance pop]                               2.4527      1.691      1.451      0.147      -0.861       5.766
artist_avg_popularity:playlist_subgenre[T.electro house]                           1.7105      1.630      1.050      0.294      -1.484       4.905
artist_avg_popularity:playlist_subgenre[T.electropop]                              4.6163      1.581      2.920      0.004       1.517       7.715
artist_avg_popularity:playlist_subgenre[T.gangster rap]                            5.6255      1.534      3.668      0.000       2.620       8.631
artist_avg_popularity:playlist_subgenre[T.hard rock]                               7.3557      1.542      4.769      0.000       4.333      10.379
artist_avg_popularity:playlist_subgenre[T.hip hop]                                 2.3611      1.733      1.363      0.173      -1.035       5.757
artist_avg_popularity:playlist_subgenre[T.hip pop]                                 3.6749      1.771      2.075      0.038       0.203       7.146
artist_avg_popularity:playlist_subgenre[T.indie poptimism]                         3.9784      1.477      2.694      0.007       1.084       6.873
artist_avg_popularity:playlist_subgenre[T.latin hip hop]                           2.9650      1.567      1.892      0.058      -0.106       6.036
artist_avg_popularity:playlist_subgenre[T.latin pop]                               5.7313      1.718      3.336      0.001       2.364       9.099
artist_avg_popularity:playlist_subgenre[T.neo soul]                                3.1149      1.480      2.104      0.035       0.213       6.017
artist_avg_popularity:playlist_subgenre[T.new jack swing]                          1.3678      1.713      0.799      0.425      -1.990       4.725
artist_avg_popularity:playlist_subgenre[T.permanent wave]                          1.2060      1.621      0.744      0.457      -1.971       4.383
artist_avg_popularity:playlist_subgenre[T.pop edm]                                 4.4241      1.818      2.434      0.015       0.861       7.987
artist_avg_popularity:playlist_subgenre[T.post-teen pop]                           2.5478      1.720      1.482      0.138      -0.823       5.918
artist_avg_popularity:playlist_subgenre[T.progressive electro house]              -1.5750      1.489     -1.058      0.290      -4.493       1.343
artist_avg_popularity:playlist_subgenre[T.reggaeton]                               3.3175      2.256      1.471      0.141      -1.104       7.739
artist_avg_popularity:playlist_subgenre[T.southern hip hop]                        4.0749      1.504      2.709      0.007       1.126       7.024
artist_avg_popularity:playlist_subgenre[T.trap]                                    5.8081      1.780      3.262      0.001       2.318       9.298
artist_avg_popularity:playlist_subgenre[T.tropical]                                7.2145      1.643      4.391      0.000       3.994      10.435
artist_avg_popularity:playlist_subgenre[T.urban contemporary]                      3.7987      1.609      2.362      0.018       0.646       6.951
playlist_avg_popularity                                                            9.8344      0.731     13.446      0.000       8.401      11.268
playlist_avg_popularity:playlist_subgenre[T.big room]                             -0.4623      1.680     -0.275      0.783      -3.756       2.831
playlist_avg_popularity:playlist_subgenre[T.classic rock]                          1.4046      0.977      1.438      0.150      -0.510       3.319
playlist_avg_popularity:playlist_subgenre[T.dance pop]                           -10.0526      2.487     -4.042      0.000     -14.927      -5.178
playlist_avg_popularity:playlist_subgenre[T.electro house]                        -2.1951      1.450     -1.513      0.130      -5.038       0.648
playlist_avg_popularity:playlist_subgenre[T.electropop]                           -0.7383      0.993     -0.744      0.457      -2.684       1.208
playlist_avg_popularity:playlist_subgenre[T.gangster rap]                         -1.4846      1.169     -1.269      0.204      -3.777       0.808
playlist_avg_popularity:playlist_subgenre[T.hard rock]                            -2.0350      1.167     -1.743      0.081      -4.323       0.253
playlist_avg_popularity:playlist_subgenre[T.hip hop]                              -4.0025      4.820     -0.830      0.406     -13.449       5.444
playlist_avg_popularity:playlist_subgenre[T.hip pop]                              -4.9599      1.129     -4.394      0.000      -7.172      -2.747
playlist_avg_popularity:playlist_subgenre[T.indie poptimism]                      -1.2618      0.941     -1.341      0.180      -3.106       0.582
playlist_avg_popularity:playlist_subgenre[T.latin hip hop]                        -4.6586      1.054     -4.418      0.000      -6.725      -2.592
playlist_avg_popularity:playlist_subgenre[T.latin pop]                            -4.1698      1.303     -3.201      0.001      -6.723      -1.616
playlist_avg_popularity:playlist_subgenre[T.neo soul]                             -2.5274      1.119     -2.258      0.024      -4.721      -0.334
playlist_avg_popularity:playlist_subgenre[T.new jack swing]                        1.5423      2.086      0.740      0.460      -2.546       5.630
playlist_avg_popularity:playlist_subgenre[T.permanent wave]                       -3.2505      2.649     -1.227      0.220      -8.443       1.942
playlist_avg_popularity:playlist_subgenre[T.pop edm]                              -0.3464      1.057     -0.328      0.743      -2.417       1.725
playlist_avg_popularity:playlist_subgenre[T.post-teen pop]                        -2.9509      1.121     -2.633      0.008      -5.147      -0.754
playlist_avg_popularity:playlist_subgenre[T.progressive electro house]            -1.0256      1.278     -0.803      0.422      -3.530       1.478
playlist_avg_popularity:playlist_subgenre[T.reggaeton]                             3.1093      1.096      2.838      0.005       0.962       5.257
playlist_avg_popularity:playlist_subgenre[T.southern hip hop]                      1.1486      1.113      1.032      0.302      -1.033       3.330
playlist_avg_popularity:playlist_subgenre[T.trap]                                 -0.8049      2.247     -0.358      0.720      -5.210       3.600
playlist_avg_popularity:playlist_subgenre[T.tropical]                             -1.7753      1.571     -1.130      0.258      -4.854       1.303
playlist_avg_popularity:playlist_subgenre[T.urban contemporary]                   -2.0328      1.005     -2.023      0.043      -4.003      -0.063
danceability                                                                       1.6226      0.894      1.816      0.069      -0.129       3.374
danceability:playlist_subgenre[T.big room]                                        -2.3248      1.204     -1.931      0.054      -4.685       0.035
danceability:playlist_subgenre[T.classic rock]                                    -0.4456      1.233     -0.361      0.718      -2.862       1.970
danceability:playlist_subgenre[T.dance pop]                                       -1.1411      1.112     -1.026      0.305      -3.321       1.039
danceability:playlist_subgenre[T.electro house]                                   -2.3115      1.082     -2.136      0.033      -4.433      -0.190
danceability:playlist_subgenre[T.electropop]                                      -1.6433      1.119     -1.469      0.142      -3.836       0.549
danceability:playlist_subgenre[T.gangster rap]                                    -2.2548      1.067     -2.112      0.035      -4.347      -0.163
danceability:playlist_subgenre[T.hard rock]                                        1.0370      1.503      0.690      0.490      -1.909       3.983
danceability:playlist_subgenre[T.hip hop]                                         -0.7775      1.049     -0.741      0.458      -2.833       1.278
danceability:playlist_subgenre[T.hip pop]                                         -1.1696      1.137     -1.028      0.304      -3.399       1.060
danceability:playlist_subgenre[T.indie poptimism]                                 -1.4242      1.089     -1.308      0.191      -3.558       0.709
danceability:playlist_subgenre[T.latin hip hop]                                   -2.2554      1.148     -1.964      0.050      -4.506      -0.005
danceability:playlist_subgenre[T.latin pop]                                        1.2333      1.123      1.098      0.272      -0.968       3.435
danceability:playlist_subgenre[T.neo soul]                                        -1.6799      1.047     -1.604      0.109      -3.733       0.373
danceability:playlist_subgenre[T.new jack swing]                                  -2.5732      1.265     -2.035      0.042      -5.052      -0.095
danceability:playlist_subgenre[T.permanent wave]                                  -0.8456      1.326     -0.638      0.524      -3.445       1.754
danceability:playlist_subgenre[T.pop edm]                                         -1.6741      1.168     -1.433      0.152      -3.963       0.615
danceability:playlist_subgenre[T.post-teen pop]                                   -0.6312      1.130     -0.559      0.576      -2.845       1.583
danceability:playlist_subgenre[T.progressive electro house]                       -1.4940      1.090     -1.371      0.170      -3.630       0.642
danceability:playlist_subgenre[T.reggaeton]                                       -0.1228      1.571     -0.078      0.938      -3.201       2.956
danceability:playlist_subgenre[T.southern hip hop]                                -0.9601      1.002     -0.958      0.338      -2.925       1.004
danceability:playlist_subgenre[T.trap]                                            -1.0850      1.094     -0.992      0.321      -3.229       1.059
danceability:playlist_subgenre[T.tropical]                                        -0.9816      1.154     -0.850      0.395      -3.244       1.281
danceability:playlist_subgenre[T.urban contemporary]                              -1.1758      1.053     -1.117      0.264      -3.239       0.887
energy                                                                            -0.5055      0.581     -0.869      0.385      -1.645       0.634
energy:playlist_subgenre[T.big room]                                               0.3530      1.214      0.291      0.771      -2.027       2.733
energy:playlist_subgenre[T.classic rock]                                          -0.3857      0.817     -0.472      0.637      -1.987       1.216
energy:playlist_subgenre[T.dance pop]                                             -1.1515      0.847     -1.359      0.174      -2.812       0.509
energy:playlist_subgenre[T.electro house]                                          0.1184      0.812      0.146      0.884      -1.473       1.710
energy:playlist_subgenre[T.electropop]                                             0.6571      0.835      0.787      0.431      -0.980       2.294
energy:playlist_subgenre[T.gangster rap]                                           0.9175      0.861      1.065      0.287      -0.771       2.606
energy:playlist_subgenre[T.hard rock]                                             -1.2571      0.844     -1.489      0.136      -2.911       0.397
energy:playlist_subgenre[T.hip hop]                                                0.0197      0.940      0.021      0.983      -1.824       1.863
energy:playlist_subgenre[T.hip pop]                                               -0.1709      1.047     -0.163      0.870      -2.222       1.880
energy:playlist_subgenre[T.indie poptimism]                                       -0.1758      0.840     -0.209      0.834      -1.821       1.470
energy:playlist_subgenre[T.latin hip hop]                                          0.0308      0.854      0.036      0.971      -1.644       1.705
energy:playlist_subgenre[T.latin pop]                                              0.1807      0.907      0.199      0.842      -1.597       1.959
energy:playlist_subgenre[T.neo soul]                                              -0.3800      0.923     -0.412      0.681      -2.189       1.429
energy:playlist_subgenre[T.new jack swing]                                        -1.2141      0.897     -1.354      0.176      -2.972       0.543
energy:playlist_subgenre[T.permanent wave]                                         1.2217      0.859      1.423      0.155      -0.461       2.905
energy:playlist_subgenre[T.pop edm]                                                0.1014      0.943      0.108      0.914      -1.747       1.950
energy:playlist_subgenre[T.post-teen pop]                                          0.0577      0.897      0.064      0.949      -1.701       1.816
energy:playlist_subgenre[T.progressive electro house]                             -0.1027      0.917     -0.112      0.911      -1.900       1.695
energy:playlist_subgenre[T.reggaeton]                                              1.2551      1.256      0.999      0.318      -1.208       3.718
energy:playlist_subgenre[T.southern hip hop]                                      -0.2111      0.823     -0.257      0.797      -1.823       1.401
energy:playlist_subgenre[T.trap]                                                   1.7872      0.885      2.019      0.044       0.052       3.522
energy:playlist_subgenre[T.tropical]                                               0.3020      0.899      0.336      0.737      -1.461       2.065
energy:playlist_subgenre[T.urban contemporary]                                    -1.0285      0.960     -1.072      0.284      -2.909       0.852
valence                                                                           -0.3394      0.610     -0.556      0.578      -1.536       0.857
valence:playlist_subgenre[T.big room]                                              0.2195      1.142      0.192      0.848      -2.020       2.459
valence:playlist_subgenre[T.classic rock]                                         -0.7716      0.902     -0.856      0.392      -2.539       0.996
valence:playlist_subgenre[T.dance pop]                                             1.0169      0.806      1.262      0.207      -0.563       2.596
valence:playlist_subgenre[T.electro house]                                         1.0694      0.782      1.367      0.171      -0.463       2.602
valence:playlist_subgenre[T.electropop]                                           -0.3087      0.793     -0.389      0.697      -1.864       1.246
valence:playlist_subgenre[T.gangster rap]                                         -0.0329      0.778     -0.042      0.966      -1.557       1.492
valence:playlist_subgenre[T.hard rock]                                            -0.9597      0.877     -1.094      0.274      -2.679       0.760
valence:playlist_subgenre[T.hip hop]                                               0.1490      0.787      0.189      0.850      -1.394       1.692
valence:playlist_subgenre[T.hip pop]                                               1.7761      0.874      2.033      0.042       0.064       3.489
valence:playlist_subgenre[T.indie poptimism]                                      -0.3856      0.796     -0.485      0.628      -1.945       1.174
valence:playlist_subgenre[T.latin hip hop]                                         0.1610      0.818      0.197      0.844      -1.443       1.765
valence:playlist_subgenre[T.latin pop]                                            -0.8767      0.884     -0.992      0.321      -2.609       0.856
valence:playlist_subgenre[T.neo soul]                                              0.7968      0.805      0.989      0.322      -0.782       2.375
valence:playlist_subgenre[T.new jack swing]                                        0.2522      1.036      0.243      0.808      -1.779       2.284
valence:playlist_subgenre[T.permanent wave]                                        0.6348      0.871      0.729      0.466      -1.073       2.343
valence:playlist_subgenre[T.pop edm]                                              -0.5850      0.893     -0.655      0.512      -2.335       1.165
valence:playlist_subgenre[T.post-teen pop]                                         0.5247      0.880      0.596      0.551      -1.199       2.249
valence:playlist_subgenre[T.progressive electro house]                             0.5102      0.805      0.634      0.526      -1.067       2.087
valence:playlist_subgenre[T.reggaeton]                                             1.2511      1.212      1.032      0.302      -1.124       3.627
valence:playlist_subgenre[T.southern hip hop]                                      0.7485      0.764      0.979      0.328      -0.750       2.247
valence:playlist_subgenre[T.trap]                                                  0.6157      0.843      0.731      0.465      -1.036       2.268
valence:playlist_subgenre[T.tropical]                                              0.4230      0.802      0.528      0.598      -1.148       1.994
valence:playlist_subgenre[T.urban contemporary]                                    2.3839      0.828      2.878      0.004       0.760       4.007
tempo                                                                             -0.0591      0.470     -0.126      0.900      -0.979       0.861
tempo:playlist_subgenre[T.big room]                                                0.0807      1.148      0.070      0.944      -2.170       2.332
tempo:playlist_subgenre[T.classic rock]                                            0.3480      0.671      0.519      0.604      -0.967       1.663
tempo:playlist_subgenre[T.dance pop]                                               0.6100      0.734      0.831      0.406      -0.830       2.049
tempo:playlist_subgenre[T.electro house]                                           0.9172      1.134      0.809      0.419      -1.305       3.140
tempo:playlist_subgenre[T.electropop]                                              0.0171      0.693      0.025      0.980      -1.342       1.376
tempo:playlist_subgenre[T.gangster rap]                                            0.3685      0.587      0.627      0.531      -0.783       1.520
tempo:playlist_subgenre[T.hard rock]                                               0.6169      0.637      0.969      0.332      -0.631       1.865
tempo:playlist_subgenre[T.hip hop]                                                 0.0629      0.585      0.108      0.914      -1.084       1.210
tempo:playlist_subgenre[T.hip pop]                                                -0.1897      0.683     -0.278      0.781      -1.528       1.148
tempo:playlist_subgenre[T.indie poptimism]                                         0.7297      0.614      1.189      0.235      -0.473       1.933
tempo:playlist_subgenre[T.latin hip hop]                                           1.1915      0.661      1.801      0.072      -0.105       2.488
tempo:playlist_subgenre[T.latin pop]                                               0.1781      0.642      0.277      0.782      -1.081       1.437
tempo:playlist_subgenre[T.neo soul]                                                0.2423      0.605      0.400      0.689      -0.944       1.428
tempo:playlist_subgenre[T.new jack swing]                                         -0.6436      0.695     -0.925      0.355      -2.007       0.720
tempo:playlist_subgenre[T.permanent wave]                                         -0.2020      0.687     -0.294      0.769      -1.548       1.144
tempo:playlist_subgenre[T.pop edm]                                                 0.5796      0.764      0.759      0.448      -0.917       2.076
tempo:playlist_subgenre[T.post-teen pop]                                          -0.6075      0.669     -0.909      0.364      -1.918       0.703
tempo:playlist_subgenre[T.progressive electro house]                               0.3652      1.243      0.294      0.769      -2.071       2.801
tempo:playlist_subgenre[T.reggaeton]                                               1.3165      0.753      1.747      0.081      -0.160       2.793
tempo:playlist_subgenre[T.southern hip hop]                                       -0.3997      0.565     -0.708      0.479      -1.507       0.708
tempo:playlist_subgenre[T.trap]                                                   -0.3197      0.646     -0.495      0.620      -1.585       0.946
tempo:playlist_subgenre[T.tropical]                                                0.4166      0.724      0.576      0.565      -1.002       1.835
tempo:playlist_subgenre[T.urban contemporary]                                      0.0308      0.619      0.050      0.960      -1.182       1.243
duration_ms                                                                        1.1862      0.446      2.663      0.008       0.313       2.059
duration_ms:playlist_subgenre[T.big room]                                         -1.3682      0.784     -1.745      0.081      -2.905       0.169
duration_ms:playlist_subgenre[T.classic rock]                                     -1.3732      0.746     -1.840      0.066      -2.836       0.090
duration_ms:playlist_subgenre[T.dance pop]                                        -0.8326      0.760     -1.095      0.273      -2.322       0.657
duration_ms:playlist_subgenre[T.electro house]                                    -2.3545      0.587     -4.014      0.000      -3.504      -1.205
duration_ms:playlist_subgenre[T.electropop]                                       -1.1286      0.708     -1.595      0.111      -2.516       0.258
duration_ms:playlist_subgenre[T.gangster rap]                                     -1.1543      0.647     -1.784      0.074      -2.423       0.114
duration_ms:playlist_subgenre[T.hard rock]                                        -0.8823      0.746     -1.183      0.237      -2.344       0.579
duration_ms:playlist_subgenre[T.hip hop]                                           1.0978      0.789      1.391      0.164      -0.449       2.644
duration_ms:playlist_subgenre[T.hip pop]                                          -1.2588      0.840     -1.498      0.134      -2.906       0.388
duration_ms:playlist_subgenre[T.indie poptimism]                                  -0.3919      0.742     -0.529      0.597      -1.845       1.061
duration_ms:playlist_subgenre[T.latin hip hop]                                    -1.0417      0.652     -1.597      0.110      -2.320       0.237
duration_ms:playlist_subgenre[T.latin pop]                                        -1.4729      0.858     -1.716      0.086      -3.155       0.209
duration_ms:playlist_subgenre[T.neo soul]                                         -1.0260      0.612     -1.677      0.094      -2.225       0.173
duration_ms:playlist_subgenre[T.new jack swing]                                   -0.1686      0.842     -0.200      0.841      -1.819       1.482
duration_ms:playlist_subgenre[T.permanent wave]                                   -1.2799      0.762     -1.680      0.093      -2.773       0.213
duration_ms:playlist_subgenre[T.pop edm]                                          -2.3247      0.830     -2.801      0.005      -3.951      -0.698
duration_ms:playlist_subgenre[T.post-teen pop]                                    -1.2095      0.936     -1.292      0.196      -3.044       0.625
duration_ms:playlist_subgenre[T.progressive electro house]                        -2.3513      0.719     -3.268      0.001      -3.762      -0.941
duration_ms:playlist_subgenre[T.reggaeton]                                         0.7129      0.955      0.746      0.456      -1.160       2.585
duration_ms:playlist_subgenre[T.southern hip hop]                                 -0.6858      0.603     -1.136      0.256      -1.869       0.497
duration_ms:playlist_subgenre[T.trap]                                             -1.0799      0.737     -1.464      0.143      -2.525       0.365
duration_ms:playlist_subgenre[T.tropical]                                         -1.0692      0.747     -1.432      0.152      -2.533       0.394
duration_ms:playlist_subgenre[T.urban contemporary]                               -0.6038      0.659     -0.917      0.359      -1.895       0.687
artist_hit_rate                                                                   -1.4088      1.217     -1.158      0.247      -3.794       0.976
artist_hit_rate:playlist_subgenre[T.big room]                                     -5.5373      2.295     -2.412      0.016     -10.036      -1.038
artist_hit_rate:playlist_subgenre[T.classic rock]                                  0.9750      1.669      0.584      0.559      -2.296       4.246
artist_hit_rate:playlist_subgenre[T.dance pop]                                     1.4477      1.552      0.933      0.351      -1.594       4.490
artist_hit_rate:playlist_subgenre[T.electro house]                                -0.6717      2.134     -0.315      0.753      -4.855       3.511
artist_hit_rate:playlist_subgenre[T.electropop]                                   -1.1850      1.544     -0.767      0.443      -4.212       1.842
artist_hit_rate:playlist_subgenre[T.gangster rap]                                 -3.6611      1.644     -2.227      0.026      -6.884      -0.439
artist_hit_rate:playlist_subgenre[T.hard rock]                                    -2.9241      1.685     -1.736      0.083      -6.226       0.378
artist_hit_rate:playlist_subgenre[T.hip hop]                                       0.1033      1.555      0.066      0.947      -2.944       3.151
artist_hit_rate:playlist_subgenre[T.hip pop]                                       4.9828      1.774      2.809      0.005       1.506       8.460
artist_hit_rate:playlist_subgenre[T.indie poptimism]                              -0.5269      1.544     -0.341      0.733      -3.554       2.500
artist_hit_rate:playlist_subgenre[T.latin hip hop]                                 2.3650      1.630      1.451      0.147      -0.830       5.560
artist_hit_rate:playlist_subgenre[T.latin pop]                                     2.3601      1.554      1.519      0.129      -0.686       5.406
artist_hit_rate:playlist_subgenre[T.neo soul]                                     -2.0838      1.668     -1.249      0.212      -5.353       1.185
artist_hit_rate:playlist_subgenre[T.new jack swing]                               -0.4752      2.230     -0.213      0.831      -4.846       3.895
artist_hit_rate:playlist_subgenre[T.permanent wave]                                2.1571      1.613      1.338      0.181      -1.004       5.318
artist_hit_rate:playlist_subgenre[T.pop edm]                                      -2.8291      1.686     -1.678      0.093      -6.133       0.475
artist_hit_rate:playlist_subgenre[T.post-teen pop]                                 3.6934      1.602      2.305      0.021       0.553       6.834
artist_hit_rate:playlist_subgenre[T.progressive electro house]                    -0.7408      1.979     -0.374      0.708      -4.620       3.139
artist_hit_rate:playlist_subgenre[T.reggaeton]                                    -2.5181      1.791     -1.406      0.160      -6.028       0.991
artist_hit_rate:playlist_subgenre[T.southern hip hop]                              1.1692      1.582      0.739      0.460      -1.931       4.270
artist_hit_rate:playlist_subgenre[T.trap]                                         -1.9553      1.630     -1.200      0.230      -5.150       1.239
artist_hit_rate:playlist_subgenre[T.tropical]                                     -0.6383      1.903     -0.335      0.737      -4.368       3.091
artist_hit_rate:playlist_subgenre[T.urban contemporary]                           -1.2168      1.538     -0.791      0.429      -4.231       1.797
artist_n_tracks                                                                    1.0025      0.652      1.538      0.124      -0.275       2.280
artist_n_tracks:playlist_subgenre[T.big room]                                      0.5712      0.866      0.659      0.510      -1.126       2.269
artist_n_tracks:playlist_subgenre[T.classic rock]                                 -1.3421      0.986     -1.361      0.173      -3.274       0.590
artist_n_tracks:playlist_subgenre[T.dance pop]                                     3.3154      0.936      3.541      0.000       1.480       5.151
artist_n_tracks:playlist_subgenre[T.electro house]                                 0.2556      0.870      0.294      0.769      -1.449       1.960
artist_n_tracks:playlist_subgenre[T.electropop]                                   -2.1399      0.894     -2.393      0.017      -3.893      -0.387
artist_n_tracks:playlist_subgenre[T.gangster rap]                                 -1.5403      0.880     -1.749      0.080      -3.266       0.185
artist_n_tracks:playlist_subgenre[T.hard rock]                                    -0.8729      0.923     -0.946      0.344      -2.682       0.937
artist_n_tracks:playlist_subgenre[T.hip hop]                                       0.7471      0.911      0.820      0.412      -1.039       2.533
artist_n_tracks:playlist_subgenre[T.hip pop]                                      -1.9162      1.119     -1.712      0.087      -4.110       0.278
artist_n_tracks:playlist_subgenre[T.indie poptimism]                              -0.2630      0.891     -0.295      0.768      -2.009       1.483
artist_n_tracks:playlist_subgenre[T.latin hip hop]                                -3.0028      0.889     -3.379      0.001      -4.744      -1.261
artist_n_tracks:playlist_subgenre[T.latin pop]                                    -0.1056      0.924     -0.114      0.909      -1.916       1.705
artist_n_tracks:playlist_subgenre[T.neo soul]                                     -1.5179      0.831     -1.826      0.068      -3.147       0.111
artist_n_tracks:playlist_subgenre[T.new jack swing]                               -1.8331      1.027     -1.785      0.074      -3.846       0.179
artist_n_tracks:playlist_subgenre[T.permanent wave]                                1.4990      0.965      1.553      0.120      -0.393       3.390
artist_n_tracks:playlist_subgenre[T.pop edm]                                      -2.0537      0.981     -2.093      0.036      -3.977      -0.131
artist_n_tracks:playlist_subgenre[T.post-teen pop]                                 1.0652      1.033      1.031      0.303      -0.960       3.091
artist_n_tracks:playlist_subgenre[T.progressive electro house]                    -2.7579      0.839     -3.288      0.001      -4.402      -1.114
artist_n_tracks:playlist_subgenre[T.reggaeton]                                     1.9324      1.146      1.686      0.092      -0.315       4.179
artist_n_tracks:playlist_subgenre[T.southern hip hop]                             -0.0374      0.839     -0.045      0.964      -1.681       1.606
artist_n_tracks:playlist_subgenre[T.trap]                                         -0.3231      0.955     -0.338      0.735      -2.195       1.549
artist_n_tracks:playlist_subgenre[T.tropical]                                     -1.1237      0.970     -1.159      0.247      -3.024       0.777
artist_n_tracks:playlist_subgenre[T.urban contemporary]                            1.7128      0.895      1.914      0.056      -0.041       3.467
I(artist_avg_popularity ** 2)                                                      3.0143      0.313      9.635      0.000       2.401       3.627
I(artist_avg_popularity ** 2):playlist_subgenre[T.big room]                        0.6817      0.479      1.422      0.155      -0.258       1.621
I(artist_avg_popularity ** 2):playlist_subgenre[T.classic rock]                    0.6366      0.478      1.330      0.183      -0.301       1.575
I(artist_avg_popularity ** 2):playlist_subgenre[T.dance pop]                       0.6401      0.622      1.028      0.304      -0.580       1.860
I(artist_avg_popularity ** 2):playlist_subgenre[T.electro house]                   0.7843      0.442      1.774      0.076      -0.082       1.651
I(artist_avg_popularity ** 2):playlist_subgenre[T.electropop]                      1.0065      0.420      2.399      0.016       0.184       1.829
I(artist_avg_popularity ** 2):playlist_subgenre[T.gangster rap]                    1.2797      0.420      3.044      0.002       0.456       2.104
I(artist_avg_popularity ** 2):playlist_subgenre[T.hard rock]                       1.9650      0.454      4.329      0.000       1.075       2.855
I(artist_avg_popularity ** 2):playlist_subgenre[T.hip hop]                         0.8391      0.809      1.037      0.300      -0.746       2.425
I(artist_avg_popularity ** 2):playlist_subgenre[T.hip pop]                         0.8694      0.496      1.753      0.080      -0.103       1.842
I(artist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism]                 1.1244      0.414      2.716      0.007       0.313       1.936
I(artist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop]                   0.5825      0.406      1.433      0.152      -0.214       1.379
I(artist_avg_popularity ** 2):playlist_subgenre[T.latin pop]                       1.5068      0.481      3.130      0.002       0.563       2.451
I(artist_avg_popularity ** 2):playlist_subgenre[T.neo soul]                        0.6816      0.393      1.736      0.083      -0.088       1.451
I(artist_avg_popularity ** 2):playlist_subgenre[T.new jack swing]                  0.5731      0.501      1.143      0.253      -0.409       1.556
I(artist_avg_popularity ** 2):playlist_subgenre[T.permanent wave]                  0.6519      0.685      0.951      0.341      -0.691       1.995
I(artist_avg_popularity ** 2):playlist_subgenre[T.pop edm]                         1.1644      0.484      2.408      0.016       0.217       2.112
I(artist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop]                   0.7841      0.532      1.474      0.140      -0.258       1.827
I(artist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house]      -0.0892      0.395     -0.226      0.821      -0.864       0.685
I(artist_avg_popularity ** 2):playlist_subgenre[T.reggaeton]                       1.4927      0.687      2.174      0.030       0.147       2.838
I(artist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop]                1.1265      0.422      2.669      0.008       0.299       1.954
I(artist_avg_popularity ** 2):playlist_subgenre[T.trap]                            1.4812      0.554      2.676      0.007       0.396       2.566
I(artist_avg_popularity ** 2):playlist_subgenre[T.tropical]                        2.4073      0.602      4.001      0.000       1.228       3.587
I(artist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary]              0.9372      0.445      2.107      0.035       0.066       1.809
I(playlist_avg_popularity ** 2)                                                    2.1446      0.198     10.819      0.000       1.756       2.533
I(playlist_avg_popularity ** 2):playlist_subgenre[T.big room]                     -1.5693      0.642     -2.445      0.014      -2.827      -0.311
I(playlist_avg_popularity ** 2):playlist_subgenre[T.classic rock]                  5.1724      1.149      4.501      0.000       2.920       7.425
I(playlist_avg_popularity ** 2):playlist_subgenre[T.dance pop]                     4.4731      1.703      2.627      0.009       1.135       7.811
I(playlist_avg_popularity ** 2):playlist_subgenre[T.electro house]                -1.9415      0.621     -3.127      0.002      -3.158      -0.725
I(playlist_avg_popularity ** 2):playlist_subgenre[T.electropop]                    1.5226      0.375      4.058      0.000       0.787       2.258
I(playlist_avg_popularity ** 2):playlist_subgenre[T.gangster rap]                  0.0970      0.795      0.122      0.903      -1.462       1.656
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hard rock]                    -1.6179      0.406     -3.982      0.000      -2.414      -0.822
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip hop]                       1.9823      2.647      0.749      0.454      -3.206       7.170
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip pop]                       1.1151      1.087      1.026      0.305      -1.015       3.245
I(playlist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism]               0.5326      0.749      0.711      0.477      -0.936       2.001
I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop]                -1.0956      0.264     -4.151      0.000      -1.613      -0.578
I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin pop]                     1.4728      1.078      1.366      0.172      -0.640       3.586
I(playlist_avg_popularity ** 2):playlist_subgenre[T.neo soul]                     -0.4169      0.299     -1.396      0.163      -1.002       0.169
I(playlist_avg_popularity ** 2):playlist_subgenre[T.new jack swing]                0.1140      1.115      0.102      0.919      -2.071       2.299
I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave]                3.0497      2.077      1.469      0.142      -1.021       7.120
I(playlist_avg_popularity ** 2):playlist_subgenre[T.pop edm]                       0.6878      0.746      0.921      0.357      -0.775       2.151
I(playlist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop]                 2.3608      0.700      3.374      0.001       0.989       3.732
I(playlist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house]    -0.8737      0.391     -2.236      0.025      -1.639      -0.108
I(playlist_avg_popularity ** 2):playlist_subgenre[T.reggaeton]                    -1.3945      1.200     -1.162      0.245      -3.747       0.958
I(playlist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop]              3.1843      0.879      3.622      0.000       1.461       4.907
I(playlist_avg_popularity ** 2):playlist_subgenre[T.trap]                         -0.0560      1.907     -0.029      0.977      -3.794       3.682
I(playlist_avg_popularity ** 2):playlist_subgenre[T.tropical]                     -4.4527      2.271     -1.960      0.050      -8.905      -0.001
I(playlist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary]            1.0602      0.835      1.269      0.204      -0.577       2.698
I(danceability ** 2)                                                               0.2649      0.323      0.819      0.413      -0.369       0.898
I(danceability ** 2):playlist_subgenre[T.big room]                                 0.1994      0.539      0.370      0.711      -0.857       1.256
I(danceability ** 2):playlist_subgenre[T.classic rock]                             0.2881      0.463      0.623      0.533      -0.618       1.195
I(danceability ** 2):playlist_subgenre[T.dance pop]                                0.5113      0.548      0.934      0.350      -0.562       1.585
I(danceability ** 2):playlist_subgenre[T.electro house]                           -0.0877      0.549     -0.160      0.873      -1.165       0.989
I(danceability ** 2):playlist_subgenre[T.electropop]                              -0.0362      0.480     -0.075      0.940      -0.977       0.905
I(danceability ** 2):playlist_subgenre[T.gangster rap]                            -0.2427      0.548     -0.442      0.658      -1.318       0.832
I(danceability ** 2):playlist_subgenre[T.hard rock]                                0.6863      0.497      1.381      0.167      -0.287       1.660
I(danceability ** 2):playlist_subgenre[T.hip hop]                                  0.0414      0.522      0.079      0.937      -0.981       1.064
I(danceability ** 2):playlist_subgenre[T.hip pop]                                 -0.0449      0.575     -0.078      0.938      -1.172       1.082
I(danceability ** 2):playlist_subgenre[T.indie poptimism]                         -0.6390      0.451     -1.418      0.156      -1.522       0.244
I(danceability ** 2):playlist_subgenre[T.latin hip hop]                            0.3075      0.641      0.480      0.631      -0.948       1.563
I(danceability ** 2):playlist_subgenre[T.latin pop]                               -0.1345      0.507     -0.265      0.791      -1.127       0.858
I(danceability ** 2):playlist_subgenre[T.neo soul]                                -0.9196      0.463     -1.986      0.047      -1.827      -0.012
I(danceability ** 2):playlist_subgenre[T.new jack swing]                          -0.4956      0.704     -0.705      0.481      -1.875       0.883
I(danceability ** 2):playlist_subgenre[T.permanent wave]                          -0.2190      0.480     -0.457      0.648      -1.159       0.721
I(danceability ** 2):playlist_subgenre[T.pop edm]                                 -0.0068      0.584     -0.012      0.991      -1.151       1.138
I(danceability ** 2):playlist_subgenre[T.post-teen pop]                            0.3897      0.509      0.766      0.444      -0.608       1.387
I(danceability ** 2):playlist_subgenre[T.progressive electro house]               -0.0953      0.532     -0.179      0.858      -1.137       0.947
I(danceability ** 2):playlist_subgenre[T.reggaeton]                                0.3314      1.049      0.316      0.752      -1.725       2.388
I(danceability ** 2):playlist_subgenre[T.southern hip hop]                         0.1014      0.427      0.237      0.813      -0.736       0.939
I(danceability ** 2):playlist_subgenre[T.trap]                                     0.1847      0.515      0.359      0.720      -0.825       1.194
I(danceability ** 2):playlist_subgenre[T.tropical]                                -0.0990      0.461     -0.215      0.830      -1.002       0.804
I(danceability ** 2):playlist_subgenre[T.urban contemporary]                      -0.0852      0.437     -0.195      0.845      -0.941       0.771
I(energy ** 2)                                                                    -0.0175      0.293     -0.060      0.952      -0.592       0.557
I(energy ** 2):playlist_subgenre[T.big room]                                      -1.4620      0.889     -1.645      0.100      -3.204       0.280
I(energy ** 2):playlist_subgenre[T.classic rock]                                  -0.6209      0.489     -1.271      0.204      -1.578       0.337
I(energy ** 2):playlist_subgenre[T.dance pop]                                     -0.7165      0.497     -1.443      0.149      -1.690       0.257
I(energy ** 2):playlist_subgenre[T.electro house]                                 -0.2810      0.550     -0.511      0.610      -1.360       0.798
I(energy ** 2):playlist_subgenre[T.electropop]                                    -0.0698      0.481     -0.145      0.885      -1.013       0.873
I(energy ** 2):playlist_subgenre[T.gangster rap]                                  -0.2307      0.580     -0.398      0.691      -1.367       0.905
I(energy ** 2):playlist_subgenre[T.hard rock]                                     -0.4410      0.567     -0.778      0.436      -1.551       0.669
I(energy ** 2):playlist_subgenre[T.hip hop]                                        0.0625      0.389      0.161      0.872      -0.700       0.825
I(energy ** 2):playlist_subgenre[T.hip pop]                                        0.3128      0.536      0.584      0.560      -0.738       1.364
I(energy ** 2):playlist_subgenre[T.indie poptimism]                               -0.1241      0.402     -0.309      0.758      -0.912       0.664
I(energy ** 2):playlist_subgenre[T.latin hip hop]                                  0.3285      0.628      0.523      0.601      -0.903       1.560
I(energy ** 2):playlist_subgenre[T.latin pop]                                     -0.0364      0.474     -0.077      0.939      -0.966       0.893
I(energy ** 2):playlist_subgenre[T.neo soul]                                      -0.0741      0.408     -0.181      0.856      -0.874       0.726
I(energy ** 2):playlist_subgenre[T.new jack swing]                                -1.3440      0.546     -2.461      0.014      -2.414      -0.274
I(energy ** 2):playlist_subgenre[T.permanent wave]                                 0.3975      0.433      0.918      0.358      -0.451       1.246
I(energy ** 2):playlist_subgenre[T.pop edm]                                        0.7498      0.722      1.039      0.299      -0.665       2.165
I(energy ** 2):playlist_subgenre[T.post-teen pop]                                 -0.3882      0.523     -0.743      0.458      -1.412       0.636
I(energy ** 2):playlist_subgenre[T.progressive electro house]                     -0.2373      0.707     -0.336      0.737      -1.623       1.148
I(energy ** 2):playlist_subgenre[T.reggaeton]                                     -2.2161      1.282     -1.729      0.084      -4.728       0.296
I(energy ** 2):playlist_subgenre[T.southern hip hop]                              -0.9652      0.550     -1.755      0.079      -2.043       0.113
I(energy ** 2):playlist_subgenre[T.trap]                                          -0.0792      0.548     -0.144      0.885      -1.153       0.995
I(energy ** 2):playlist_subgenre[T.tropical]                                       0.0057      0.475      0.012      0.990      -0.926       0.937
I(energy ** 2):playlist_subgenre[T.urban contemporary]                            -0.3312      0.405     -0.818      0.414      -1.125       0.463
I(valence ** 2)                                                                   -0.5836      0.439     -1.328      0.184      -1.445       0.278
I(valence ** 2):playlist_subgenre[T.big room]                                      0.6043      0.694      0.870      0.384      -0.757       1.965
I(valence ** 2):playlist_subgenre[T.classic rock]                                  0.7081      0.668      1.060      0.289      -0.601       2.017
I(valence ** 2):playlist_subgenre[T.dance pop]                                     0.9086      0.628      1.446      0.148      -0.323       2.140
I(valence ** 2):playlist_subgenre[T.electro house]                                 0.9082      0.565      1.606      0.108      -0.200       2.017
I(valence ** 2):playlist_subgenre[T.electropop]                                    0.2253      0.606      0.372      0.710      -0.962       1.413
I(valence ** 2):playlist_subgenre[T.gangster rap]                                  0.0025      0.582      0.004      0.997      -1.138       1.144
I(valence ** 2):playlist_subgenre[T.hard rock]                                    -0.6834      0.685     -0.998      0.318      -2.025       0.658
I(valence ** 2):playlist_subgenre[T.hip hop]                                       0.7829      0.600      1.305      0.192      -0.393       1.959
I(valence ** 2):playlist_subgenre[T.hip pop]                                       0.6640      0.700      0.948      0.343      -0.708       2.036
I(valence ** 2):playlist_subgenre[T.indie poptimism]                               0.4039      0.577      0.700      0.484      -0.727       1.535
I(valence ** 2):playlist_subgenre[T.latin hip hop]                                 0.8305      0.649      1.280      0.200      -0.441       2.102
I(valence ** 2):playlist_subgenre[T.latin pop]                                     0.5437      0.665      0.818      0.413      -0.759       1.847
I(valence ** 2):playlist_subgenre[T.neo soul]                                      0.8787      0.621      1.415      0.157      -0.339       2.096
I(valence ** 2):playlist_subgenre[T.new jack swing]                                0.8117      0.764      1.063      0.288      -0.685       2.308
I(valence ** 2):playlist_subgenre[T.permanent wave]                                0.6438      0.654      0.985      0.325      -0.637       1.925
I(valence ** 2):playlist_subgenre[T.pop edm]                                       0.6054      0.674      0.899      0.369      -0.715       1.926
I(valence ** 2):playlist_subgenre[T.post-teen pop]                                 1.1934      0.699      1.707      0.088      -0.177       2.563
I(valence ** 2):playlist_subgenre[T.progressive electro house]                     0.6819      0.564      1.210      0.226      -0.423       1.787
I(valence ** 2):playlist_subgenre[T.reggaeton]                                     0.0714      0.933      0.077      0.939      -1.758       1.901
I(valence ** 2):playlist_subgenre[T.southern hip hop]                              1.0214      0.604      1.692      0.091      -0.162       2.204
I(valence ** 2):playlist_subgenre[T.trap]                                          1.2265      0.622      1.972      0.049       0.007       2.446
I(valence ** 2):playlist_subgenre[T.tropical]                                      0.3562      0.620      0.574      0.566      -0.860       1.572
I(valence ** 2):playlist_subgenre[T.urban contemporary]                            1.1186      0.607      1.842      0.066      -0.072       2.309
I(tempo ** 2)                                                                      0.0550      0.094      0.585      0.558      -0.129       0.239
I(tempo ** 2):playlist_subgenre[T.big room]                                       -0.8050      0.728     -1.106      0.269      -2.232       0.622
I(tempo ** 2):playlist_subgenre[T.classic rock]                                   -0.6458      0.395     -1.634      0.102      -1.420       0.129
I(tempo ** 2):playlist_subgenre[T.dance pop]                                      -0.0482      0.419     -0.115      0.908      -0.870       0.773
I(tempo ** 2):playlist_subgenre[T.electro house]                                  -0.2538      0.666     -0.381      0.703      -1.559       1.052
I(tempo ** 2):playlist_subgenre[T.electropop]                                     -1.0798      0.439     -2.459      0.014      -1.940      -0.219
I(tempo ** 2):playlist_subgenre[T.gangster rap]                                   -0.2450      0.367     -0.668      0.504      -0.964       0.474
I(tempo ** 2):playlist_subgenre[T.hard rock]                                      -0.0993      0.387     -0.256      0.798      -0.858       0.659
I(tempo ** 2):playlist_subgenre[T.hip hop]                                         0.1026      0.312      0.329      0.742      -0.508       0.713
I(tempo ** 2):playlist_subgenre[T.hip pop]                                        -0.3362      0.416     -0.809      0.419      -1.151       0.479
I(tempo ** 2):playlist_subgenre[T.indie poptimism]                                 0.1841      0.349      0.527      0.598      -0.500       0.868
I(tempo ** 2):playlist_subgenre[T.latin hip hop]                                  -0.5719      0.390     -1.466      0.143      -1.336       0.193
I(tempo ** 2):playlist_subgenre[T.latin pop]                                       0.2194      0.408      0.537      0.591      -0.581       1.020
I(tempo ** 2):playlist_subgenre[T.neo soul]                                       -0.3225      0.301     -1.070      0.284      -0.913       0.268
I(tempo ** 2):playlist_subgenre[T.new jack swing]                                  0.0637      0.403      0.158      0.874      -0.725       0.853
I(tempo ** 2):playlist_subgenre[T.permanent wave]                                  0.3241      0.365      0.889      0.374      -0.391       1.039
I(tempo ** 2):playlist_subgenre[T.pop edm]                                        -0.8973      0.515     -1.742      0.082      -1.907       0.112
I(tempo ** 2):playlist_subgenre[T.post-teen pop]                                   0.6401      0.403      1.589      0.112      -0.150       1.430
I(tempo ** 2):playlist_subgenre[T.progressive electro house]                       1.3411      0.828      1.619      0.105      -0.282       2.964
I(tempo ** 2):playlist_subgenre[T.reggaeton]                                      -0.8134      0.610     -1.333      0.182      -2.009       0.382
I(tempo ** 2):playlist_subgenre[T.southern hip hop]                               -0.0441      0.324     -0.136      0.892      -0.679       0.591
I(tempo ** 2):playlist_subgenre[T.trap]                                            0.9511      0.444      2.142      0.032       0.081       1.822
I(tempo ** 2):playlist_subgenre[T.tropical]                                       -0.1804      0.491     -0.367      0.714      -1.144       0.783
I(tempo ** 2):playlist_subgenre[T.urban contemporary]                             -0.1039      0.333     -0.312      0.755      -0.756       0.548
I(duration_ms ** 2)                                                               -0.0027      0.171     -0.016      0.987      -0.337       0.332
I(duration_ms ** 2):playlist_subgenre[T.big room]                                 -0.3272      0.525     -0.623      0.533      -1.356       0.702
I(duration_ms ** 2):playlist_subgenre[T.classic rock]                              0.0377      0.359      0.105      0.916      -0.666       0.742
I(duration_ms ** 2):playlist_subgenre[T.dance pop]                                 0.2462      0.451      0.546      0.585      -0.638       1.131
I(duration_ms ** 2):playlist_subgenre[T.electro house]                             0.0293      0.202      0.145      0.884      -0.366       0.425
I(duration_ms ** 2):playlist_subgenre[T.electropop]                               -0.3959      0.350     -1.131      0.258      -1.082       0.290
I(duration_ms ** 2):playlist_subgenre[T.gangster rap]                              0.1425      0.305      0.467      0.641      -0.456       0.741
I(duration_ms ** 2):playlist_subgenre[T.hard rock]                                -0.4932      0.402     -1.225      0.220      -1.282       0.296
I(duration_ms ** 2):playlist_subgenre[T.hip hop]                                   0.3407      0.262      1.303      0.193      -0.172       0.853
I(duration_ms ** 2):playlist_subgenre[T.hip pop]                                   0.0297      0.381      0.078      0.938      -0.718       0.777
I(duration_ms ** 2):playlist_subgenre[T.indie poptimism]                           0.3458      0.541      0.639      0.523      -0.715       1.407
I(duration_ms ** 2):playlist_subgenre[T.latin hip hop]                             0.2107      0.318      0.663      0.507      -0.412       0.834
I(duration_ms ** 2):playlist_subgenre[T.latin pop]                                -1.5357      0.447     -3.438      0.001      -2.411      -0.660
I(duration_ms ** 2):playlist_subgenre[T.neo soul]                                 -0.1453      0.299     -0.486      0.627      -0.731       0.441
I(duration_ms ** 2):playlist_subgenre[T.new jack swing]                            0.0824      0.299      0.275      0.783      -0.504       0.669
I(duration_ms ** 2):playlist_subgenre[T.permanent wave]                            0.3317      0.421      0.788      0.430      -0.493       1.156
I(duration_ms ** 2):playlist_subgenre[T.pop edm]                                  -0.4510      0.537     -0.840      0.401      -1.503       0.601
I(duration_ms ** 2):playlist_subgenre[T.post-teen pop]                            -0.3891      0.357     -1.091      0.275      -1.088       0.310
I(duration_ms ** 2):playlist_subgenre[T.progressive electro house]                 0.4580      0.321      1.428      0.153      -0.171       1.086
I(duration_ms ** 2):playlist_subgenre[T.reggaeton]                                 0.3285      0.624      0.526      0.599      -0.895       1.552
I(duration_ms ** 2):playlist_subgenre[T.southern hip hop]                          0.1558      0.239      0.653      0.514      -0.312       0.623
I(duration_ms ** 2):playlist_subgenre[T.trap]                                     -0.3550      0.419     -0.848      0.397      -1.176       0.466
I(duration_ms ** 2):playlist_subgenre[T.tropical]                                 -0.0558      0.299     -0.186      0.852      -0.643       0.531
I(duration_ms ** 2):playlist_subgenre[T.urban contemporary]                       -0.0390      0.312     -0.125      0.901      -0.651       0.573
I(artist_hit_rate ** 2)                                                            0.9848      0.438      2.249      0.025       0.126       1.843
I(artist_hit_rate ** 2):playlist_subgenre[T.big room]                              1.8300      1.342      1.364      0.173      -0.800       4.460
I(artist_hit_rate ** 2):playlist_subgenre[T.classic rock]                         -0.1991      0.634     -0.314      0.753      -1.441       1.043
I(artist_hit_rate ** 2):playlist_subgenre[T.dance pop]                            -0.7435      0.525     -1.417      0.156      -1.772       0.285
I(artist_hit_rate ** 2):playlist_subgenre[T.electro house]                        -0.5505      1.071     -0.514      0.607      -2.650       1.549
I(artist_hit_rate ** 2):playlist_subgenre[T.electropop]                            0.0337      0.528      0.064      0.949      -1.002       1.069
I(artist_hit_rate ** 2):playlist_subgenre[T.gangster rap]                          0.3181      0.583      0.546      0.585      -0.824       1.460
I(artist_hit_rate ** 2):playlist_subgenre[T.hard rock]                             0.4292      0.663      0.647      0.518      -0.871       1.730
I(artist_hit_rate ** 2):playlist_subgenre[T.hip hop]                              -0.5786      0.510     -1.135      0.257      -1.578       0.421
I(artist_hit_rate ** 2):playlist_subgenre[T.hip pop]                              -1.4940      0.575     -2.597      0.009      -2.622      -0.366
I(artist_hit_rate ** 2):playlist_subgenre[T.indie poptimism]                      -0.2484      0.571     -0.435      0.664      -1.367       0.871
I(artist_hit_rate ** 2):playlist_subgenre[T.latin hip hop]                        -0.9207      0.581     -1.585      0.113      -2.059       0.218
I(artist_hit_rate ** 2):playlist_subgenre[T.latin pop]                            -0.9918      0.513     -1.934      0.053      -1.997       0.013
I(artist_hit_rate ** 2):playlist_subgenre[T.neo soul]                              0.7899      0.661      1.194      0.232      -0.506       2.086
I(artist_hit_rate ** 2):playlist_subgenre[T.new jack swing]                       -0.3868      2.420     -0.160      0.873      -5.130       4.357
I(artist_hit_rate ** 2):playlist_subgenre[T.permanent wave]                       -1.0127      0.558     -1.814      0.070      -2.107       0.081
I(artist_hit_rate ** 2):playlist_subgenre[T.pop edm]                               0.0581      0.601      0.097      0.923      -1.121       1.237
I(artist_hit_rate ** 2):playlist_subgenre[T.post-teen pop]                        -1.5462      0.538     -2.873      0.004      -2.601      -0.491
I(artist_hit_rate ** 2):playlist_subgenre[T.progressive electro house]            -1.0285      1.160     -0.886      0.375      -3.303       1.246
I(artist_hit_rate ** 2):playlist_subgenre[T.reggaeton]                             0.2030      0.586      0.346      0.729      -0.946       1.352
I(artist_hit_rate ** 2):playlist_subgenre[T.southern hip hop]                     -1.7004      0.693     -2.455      0.014      -3.058      -0.343
I(artist_hit_rate ** 2):playlist_subgenre[T.trap]                                  0.0034      0.563      0.006      0.995      -1.099       1.106
I(artist_hit_rate ** 2):playlist_subgenre[T.tropical]                             -0.0036      0.726     -0.005      0.996      -1.427       1.420
I(artist_hit_rate ** 2):playlist_subgenre[T.urban contemporary]                   -0.1060      0.521     -0.204      0.839      -1.127       0.915
I(artist_n_tracks ** 2)                                                           -0.6600      0.325     -2.028      0.043      -1.298      -0.022
I(artist_n_tracks ** 2):playlist_subgenre[T.big room]                              0.4506      0.554      0.814      0.416      -0.635       1.536
I(artist_n_tracks ** 2):playlist_subgenre[T.classic rock]                          0.7995      0.576      1.389      0.165      -0.329       1.928
I(artist_n_tracks ** 2):playlist_subgenre[T.dance pop]                             0.6981      0.536      1.303      0.193      -0.352       1.748
I(artist_n_tracks ** 2):playlist_subgenre[T.electro house]                         0.7114      0.520      1.369      0.171      -0.307       1.730
I(artist_n_tracks ** 2):playlist_subgenre[T.electropop]                            1.7907      0.534      3.353      0.001       0.744       2.837
I(artist_n_tracks ** 2):playlist_subgenre[T.gangster rap]                          0.8635      0.574      1.504      0.132      -0.261       1.988
I(artist_n_tracks ** 2):playlist_subgenre[T.hard rock]                             0.3207      0.628      0.511      0.610      -0.910       1.552
I(artist_n_tracks ** 2):playlist_subgenre[T.hip hop]                              -0.4291      0.560     -0.766      0.444      -1.527       0.669
I(artist_n_tracks ** 2):playlist_subgenre[T.hip pop]                              -0.4483      0.808     -0.555      0.579      -2.032       1.135
I(artist_n_tracks ** 2):playlist_subgenre[T.indie poptimism]                       1.1739      0.693      1.695      0.090      -0.184       2.532
I(artist_n_tracks ** 2):playlist_subgenre[T.latin hip hop]                         1.1132      0.575      1.937      0.053      -0.013       2.240
I(artist_n_tracks ** 2):playlist_subgenre[T.latin pop]                             2.3191      0.634      3.656      0.000       1.076       3.563
I(artist_n_tracks ** 2):playlist_subgenre[T.neo soul]                             -0.3795      0.718     -0.528      0.597      -1.787       1.028
I(artist_n_tracks ** 2):playlist_subgenre[T.new jack swing]                        0.3191      0.770      0.414      0.679      -1.190       1.828
I(artist_n_tracks ** 2):playlist_subgenre[T.permanent wave]                        1.1494      0.745      1.543      0.123      -0.310       2.609
I(artist_n_tracks ** 2):playlist_subgenre[T.pop edm]                               2.1646      0.590      3.669      0.000       1.008       3.321
I(artist_n_tracks ** 2):playlist_subgenre[T.post-teen pop]                        -0.5837      0.672     -0.869      0.385      -1.900       0.733
I(artist_n_tracks ** 2):playlist_subgenre[T.progressive electro house]             1.1728      0.509      2.302      0.021       0.174       2.171
I(artist_n_tracks ** 2):playlist_subgenre[T.reggaeton]                            -0.4667      0.603     -0.774      0.439      -1.649       0.715
I(artist_n_tracks ** 2):playlist_subgenre[T.southern hip hop]                     -0.0208      0.552     -0.038      0.970      -1.103       1.061
I(artist_n_tracks ** 2):playlist_subgenre[T.trap]                                 -0.1617      0.654     -0.247      0.805      -1.443       1.120
I(artist_n_tracks ** 2):playlist_subgenre[T.tropical]                             -1.1311      0.707     -1.599      0.110      -2.518       0.255
I(artist_n_tracks ** 2):playlist_subgenre[T.urban contemporary]                   -0.0611      0.591     -0.103      0.918      -1.219       1.097
==============================================================================
Omnibus:                     2088.556   Durbin-Watson:                   1.742
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4311.685
Skew:                          -0.499   Prob(JB):                         0.00
Kurtosis:                       4.629   Cond. No.                         403.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

How many coefficients were estimated?

m_7.params.size

456

m_7.params[m_7.pvalues < 0.05].size

94

m_7.params[m_7.pvalues < 0.05].sort_values(key=abs,ascending=False)

Intercept                                                                         36.264634
artist_avg_popularity                                                             19.577285
playlist_avg_popularity:playlist_subgenre[T.dance pop]                           -10.052623
playlist_avg_popularity                                                            9.834377
playlist_subgenre[T.trap]                                                         -8.431859
                                                                                    ...    
I(tempo ** 2):playlist_subgenre[T.trap]                                            0.951109
I(artist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary]              0.937206
I(danceability ** 2):playlist_subgenre[T.neo soul]                                -0.919639
I(playlist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house]    -0.873681
I(artist_n_tracks ** 2)                                                           -0.659975
Length: 94, dtype: float64

m_7.params[m_7.pvalues < 0.05].sort_values(ascending=False)[1:3]

artist_avg_popularity      19.577285
playlist_avg_popularity     9.834377
dtype: float64

print(f'R squared: {m_7.rsquared}, RMSE: {m_7.mse_resid**0.5}')

R squared: 0.6239669509284791, RMSE: 14.650902453727106

viz_fitted_vs_actual(m_7.fittedvalues, spotify_model['track_popularity'], 'Polynomial Interaction Model')

There is clear improvement with Polynomial interaction model over the ones before. More points are getting closer to the redline which indciates better performance.

Extra interactiont terms and complexity between polynomial and categorical.

f_8 = "track_popularity ~ \
  (artist_avg_popularity + playlist_avg_popularity + danceability + energy + valence + \
   tempo + duration_ms + artist_hit_rate + artist_n_tracks)*playlist_subgenre + \
  (I(artist_avg_popularity**2) + I(playlist_avg_popularity**2) + I(danceability**2) + I(energy**2) + \
  I(valence**2) + I(tempo**2) + I(duration_ms**2) + \
  I(artist_hit_rate**2) + I(artist_n_tracks**2))*playlist_subgenre + \
  (I(artist_avg_popularity**3) + I(playlist_avg_popularity**3) + I(danceability**3) + I(energy**3) + \
  I(valence**3) + I(tempo**3) + I(duration_ms**3) + \
  I(artist_hit_rate**3) + I(artist_n_tracks**3))*playlist_subgenre + \
  artist_avg_popularity*I(artist_avg_popularity**2)*playlist_subgenre + \
  artist_avg_popularity*I(artist_avg_popularity**3)*playlist_subgenre + \
  I(artist_avg_popularity**2)*I(artist_avg_popularity**3)*playlist_subgenre + \
  playlist_avg_popularity*I(playlist_avg_popularity**2)*playlist_subgenre + \
  playlist_avg_popularity*I(playlist_avg_popularity**3)*playlist_subgenre + \
  I(playlist_avg_popularity**2)*I(playlist_avg_popularity**3)*playlist_subgenre + \
  danceability*I(danceability**2)*playlist_subgenre + \
  danceability*I(danceability**3)*playlist_subgenre + \
  I(danceability**2)*I(danceability**3)*playlist_subgenre + \
  energy*I(energy**2)*playlist_subgenre + \
  energy*I(energy**3)*playlist_subgenre + \
  I(energy**2)*I(energy**3)*playlist_subgenre + \
  valence*I(valence**2)*playlist_subgenre + \
  valence*I(valence**3)*playlist_subgenre + \
  I(valence**2)*I(valence**3)*playlist_subgenre + \
  tempo*I(tempo**2)*playlist_subgenre + \
  tempo*I(tempo**3)*playlist_subgenre + \
  I(tempo**2)*I(tempo**3)*playlist_subgenre + \
  duration_ms*I(duration_ms**2)*playlist_subgenre + \
  duration_ms*I(duration_ms**3)*playlist_subgenre + \
  I(duration_ms**2)*I(duration_ms**3)*playlist_subgenre + \
  artist_hit_rate*I(artist_hit_rate**2)*playlist_subgenre + \
  artist_hit_rate*I(artist_hit_rate**3)*playlist_subgenre + \
  I(artist_hit_rate**2)*I(artist_hit_rate**3)*playlist_subgenre + \
  artist_n_tracks*I(artist_n_tracks**2)*playlist_subgenre + \
  artist_n_tracks*I(artist_n_tracks**3)*playlist_subgenre + \
  I(artist_n_tracks**2)*I(artist_n_tracks**3)*playlist_subgenre"

m_8 = fit_ols(f_8, spotify_model)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       track_popularity   R-squared:                       0.640
Model:                            OLS   Adj. R-squared:                  0.626
Method:                 Least Squares   F-statistic:                     44.00
Date:                Wed, 10 Dec 2025   Prob (F-statistic):               0.00
Time:                        06:30:02   Log-Likelihood:            -1.1548e+05
No. Observations:               28352   AIC:                         2.332e+05
Df Residuals:                   27248   BIC:                         2.423e+05
Df Model:                        1103                                         
Covariance Type:            nonrobust                                         
==================================================================================================================================================================================
                                                                                                                     coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Intercept                                                                                                         34.6557      2.522     13.742      0.000      29.713      39.599
playlist_subgenre[T.big room]                                                                                     -4.7624      3.971     -1.199      0.230     -12.546       3.022
playlist_subgenre[T.classic rock]                                                                                 -9.5650      3.418     -2.799      0.005     -16.264      -2.866
playlist_subgenre[T.dance pop]                                                                                     7.7352      3.740      2.068      0.039       0.404      15.066
playlist_subgenre[T.electro house]                                                                                 3.3298      4.160      0.800      0.423      -4.823      11.483
playlist_subgenre[T.electropop]                                                                                   -5.9354      3.400     -1.746      0.081     -12.599       0.729
playlist_subgenre[T.gangster rap]                                                                                 -4.9753      3.480     -1.430      0.153     -11.797       1.846
playlist_subgenre[T.hard rock]                                                                                    -0.3161      3.567     -0.089      0.929      -7.308       6.676
playlist_subgenre[T.hip hop]                                                                                      36.5264     21.712      1.682      0.093      -6.031      79.084
playlist_subgenre[T.hip pop]                                                                                      -9.6941      4.979     -1.947      0.052     -19.453       0.065
playlist_subgenre[T.indie poptimism]                                                                              -5.7996      3.472     -1.670      0.095     -12.605       1.005
playlist_subgenre[T.latin hip hop]                                                                                -7.6260      3.686     -2.069      0.039     -14.852      -0.400
playlist_subgenre[T.latin pop]                                                                                    -7.5552      3.668     -2.060      0.039     -14.745      -0.366
playlist_subgenre[T.neo soul]                                                                                     -6.7755      3.478     -1.948      0.051     -13.593       0.042
playlist_subgenre[T.new jack swing]                                                                               -4.5803      4.049     -1.131      0.258     -12.516       3.355
playlist_subgenre[T.permanent wave]                                                                                8.0959      3.997      2.025      0.043       0.261      15.931
playlist_subgenre[T.pop edm]                                                                                      -6.6616      3.872     -1.721      0.085     -14.250       0.927
playlist_subgenre[T.post-teen pop]                                                                                -3.2652      3.810     -0.857      0.391     -10.733       4.203
playlist_subgenre[T.progressive electro house]                                                                    -5.2927      3.595     -1.472      0.141     -12.340       1.754
playlist_subgenre[T.reggaeton]                                                                                    -5.2798      4.920     -1.073      0.283     -14.924       4.364
playlist_subgenre[T.southern hip hop]                                                                              0.1906      3.280      0.058      0.954      -6.238       6.619
playlist_subgenre[T.trap]                                                                                         -6.4616      3.697     -1.748      0.080     -13.707       0.784
playlist_subgenre[T.tropical]                                                                                     -3.7755      3.903     -0.967      0.333     -11.426       3.875
playlist_subgenre[T.urban contemporary]                                                                           -1.6477      4.033     -0.409      0.683      -9.553       6.258
artist_avg_popularity                                                                                             16.5742      2.229      7.437      0.000      12.206      20.943
artist_avg_popularity:playlist_subgenre[T.big room]                                                                5.7074      2.966      1.924      0.054      -0.107      11.522
artist_avg_popularity:playlist_subgenre[T.classic rock]                                                            0.5545      3.077      0.180      0.857      -5.476       6.585
artist_avg_popularity:playlist_subgenre[T.dance pop]                                                               3.2800      3.106      1.056      0.291      -2.808       9.368
artist_avg_popularity:playlist_subgenre[T.electro house]                                                           5.7114      2.934      1.947      0.052      -0.040      11.463
artist_avg_popularity:playlist_subgenre[T.electropop]                                                              4.8313      2.945      1.640      0.101      -0.941      10.604
artist_avg_popularity:playlist_subgenre[T.gangster rap]                                                            8.6288      2.841      3.037      0.002       3.061      14.197
artist_avg_popularity:playlist_subgenre[T.hard rock]                                                               8.5290      2.907      2.934      0.003       2.831      14.227
artist_avg_popularity:playlist_subgenre[T.hip hop]                                                                -0.8150      3.320     -0.245      0.806      -7.323       5.693
artist_avg_popularity:playlist_subgenre[T.hip pop]                                                                 7.1454      3.362      2.126      0.034       0.556      13.734
artist_avg_popularity:playlist_subgenre[T.indie poptimism]                                                         6.6342      2.793      2.376      0.018       1.161      12.108
artist_avg_popularity:playlist_subgenre[T.latin hip hop]                                                           8.8040      2.959      2.976      0.003       3.005      14.603
artist_avg_popularity:playlist_subgenre[T.latin pop]                                                              10.5595      3.198      3.302      0.001       4.292      16.827
artist_avg_popularity:playlist_subgenre[T.neo soul]                                                                6.2063      2.683      2.313      0.021       0.948      11.465
artist_avg_popularity:playlist_subgenre[T.new jack swing]                                                          8.4474      2.975      2.840      0.005       2.617      14.278
artist_avg_popularity:playlist_subgenre[T.permanent wave]                                                          8.7205      3.171      2.750      0.006       2.505      14.936
artist_avg_popularity:playlist_subgenre[T.pop edm]                                                                 5.8808      3.165      1.858      0.063      -0.323      12.085
artist_avg_popularity:playlist_subgenre[T.post-teen pop]                                                           8.7436      3.291      2.657      0.008       2.293      15.194
artist_avg_popularity:playlist_subgenre[T.progressive electro house]                                               3.8907      2.710      1.436      0.151      -1.421       9.202
artist_avg_popularity:playlist_subgenre[T.reggaeton]                                                               1.0426      3.901      0.267      0.789      -6.604       8.689
artist_avg_popularity:playlist_subgenre[T.southern hip hop]                                                        7.0990      2.765      2.568      0.010       1.680      12.518
artist_avg_popularity:playlist_subgenre[T.trap]                                                                    4.0024      3.369      1.188      0.235      -2.600      10.605
artist_avg_popularity:playlist_subgenre[T.tropical]                                                                9.0590      3.015      3.005      0.003       3.149      14.969
artist_avg_popularity:playlist_subgenre[T.urban contemporary]                                                      3.2027      3.026      1.059      0.290      -2.728       9.133
playlist_avg_popularity                                                                                            7.8082      1.720      4.541      0.000       4.438      11.179
playlist_avg_popularity:playlist_subgenre[T.big room]                                                             -8.9086      4.734     -1.882      0.060     -18.187       0.370
playlist_avg_popularity:playlist_subgenre[T.classic rock]                                                          7.1008      3.331      2.132      0.033       0.572      13.630
playlist_avg_popularity:playlist_subgenre[T.dance pop]                                                            -3.4008      5.072     -0.670      0.503     -13.343       6.541
playlist_avg_popularity:playlist_subgenre[T.electro house]                                                        -2.3276      3.172     -0.734      0.463      -8.544       3.889
playlist_avg_popularity:playlist_subgenre[T.electropop]                                                           -4.1414      2.427     -1.707      0.088      -8.898       0.615
playlist_avg_popularity:playlist_subgenre[T.gangster rap]                                                         -2.6495      2.625     -1.009      0.313      -7.795       2.496
playlist_avg_popularity:playlist_subgenre[T.hard rock]                                                            -0.4248      2.702     -0.157      0.875      -5.721       4.871
playlist_avg_popularity:playlist_subgenre[T.hip hop]                                                            -300.9947    160.470     -1.876      0.061    -615.524      13.535
playlist_avg_popularity:playlist_subgenre[T.hip pop]                                                              -2.6363      5.797     -0.455      0.649     -13.998       8.725
playlist_avg_popularity:playlist_subgenre[T.indie poptimism]                                                       0.8728      3.237      0.270      0.787      -5.473       7.218
playlist_avg_popularity:playlist_subgenre[T.latin hip hop]                                                        -2.8859      2.280     -1.266      0.206      -7.355       1.583
playlist_avg_popularity:playlist_subgenre[T.latin pop]                                                            -7.9874      4.062     -1.967      0.049     -15.948      -0.026
playlist_avg_popularity:playlist_subgenre[T.neo soul]                                                             -2.3801      2.571     -0.926      0.355      -7.419       2.659
playlist_avg_popularity:playlist_subgenre[T.new jack swing]                                                       -1.8235      5.109     -0.357      0.721     -11.837       8.190
playlist_avg_popularity:playlist_subgenre[T.permanent wave]                                                      -14.4854      8.821     -1.642      0.101     -31.776       2.805
playlist_avg_popularity:playlist_subgenre[T.pop edm]                                                              -0.5312      3.324     -0.160      0.873      -7.046       5.983
playlist_avg_popularity:playlist_subgenre[T.post-teen pop]                                                        40.5455     14.992      2.704      0.007      11.159      69.931
playlist_avg_popularity:playlist_subgenre[T.progressive electro house]                                             5.1345      2.684      1.913      0.056      -0.126      10.395
playlist_avg_popularity:playlist_subgenre[T.reggaeton]                                                             8.6449      4.797      1.802      0.072      -0.758      18.048
playlist_avg_popularity:playlist_subgenre[T.southern hip hop]                                                      3.8803      2.798      1.387      0.166      -1.604       9.364
playlist_avg_popularity:playlist_subgenre[T.trap]                                                                 -1.3598      7.458     -0.182      0.855     -15.979      13.259
playlist_avg_popularity:playlist_subgenre[T.tropical]                                                            -12.1565      5.276     -2.304      0.021     -22.498      -1.815
playlist_avg_popularity:playlist_subgenre[T.urban contemporary]                                                   -7.7584      3.712     -2.090      0.037     -15.034      -0.483
danceability                                                                                                       1.5729      1.556      1.011      0.312      -1.478       4.624
danceability:playlist_subgenre[T.big room]                                                                        -1.7488      2.011     -0.870      0.384      -5.690       2.192
danceability:playlist_subgenre[T.classic rock]                                                                    -0.1768      2.072     -0.085      0.932      -4.239       3.885
danceability:playlist_subgenre[T.dance pop]                                                                       -1.2252      1.933     -0.634      0.526      -5.014       2.564
danceability:playlist_subgenre[T.electro house]                                                                   -2.1256      2.046     -1.039      0.299      -6.137       1.886
danceability:playlist_subgenre[T.electropop]                                                                      -0.0008      1.884     -0.000      1.000      -3.693       3.692
danceability:playlist_subgenre[T.gangster rap]                                                                    -3.9531      2.055     -1.924      0.054      -7.980       0.074
danceability:playlist_subgenre[T.hard rock]                                                                        1.8868      2.587      0.729      0.466      -3.183       6.957
danceability:playlist_subgenre[T.hip hop]                                                                          0.4338      1.969      0.220      0.826      -3.425       4.293
danceability:playlist_subgenre[T.hip pop]                                                                         -1.3467      2.080     -0.648      0.517      -5.423       2.730
danceability:playlist_subgenre[T.indie poptimism]                                                                 -2.9556      1.835     -1.610      0.107      -6.553       0.642
danceability:playlist_subgenre[T.latin hip hop]                                                                    0.0588      2.224      0.026      0.979      -4.301       4.418
danceability:playlist_subgenre[T.latin pop]                                                                        1.0205      2.053      0.497      0.619      -3.004       5.045
danceability:playlist_subgenre[T.neo soul]                                                                        -1.3200      1.813     -0.728      0.466      -4.873       2.233
danceability:playlist_subgenre[T.new jack swing]                                                                  -4.0266      2.544     -1.583      0.113      -9.013       0.960
danceability:playlist_subgenre[T.permanent wave]                                                                  -1.9878      2.187     -0.909      0.363      -6.274       2.298
danceability:playlist_subgenre[T.pop edm]                                                                         -2.5646      1.991     -1.288      0.198      -6.467       1.338
danceability:playlist_subgenre[T.post-teen pop]                                                                    1.0596      1.971      0.538      0.591      -2.803       4.922
danceability:playlist_subgenre[T.progressive electro house]                                                       -0.8632      1.934     -0.446      0.655      -4.653       2.927
danceability:playlist_subgenre[T.reggaeton]                                                                       -4.2456      3.294     -1.289      0.198     -10.703       2.212
danceability:playlist_subgenre[T.southern hip hop]                                                                -1.9929      1.794     -1.111      0.267      -5.510       1.524
danceability:playlist_subgenre[T.trap]                                                                            -2.8977      2.026     -1.430      0.153      -6.869       1.073
danceability:playlist_subgenre[T.tropical]                                                                        -0.9115      1.979     -0.461      0.645      -4.790       2.967
danceability:playlist_subgenre[T.urban contemporary]                                                              -0.7564      1.848     -0.409      0.682      -4.378       2.865
energy                                                                                                            -1.2333      1.294     -0.953      0.341      -3.770       1.303
energy:playlist_subgenre[T.big room]                                                                               0.4963      3.334      0.149      0.882      -6.038       7.031
energy:playlist_subgenre[T.classic rock]                                                                          -1.0395      1.779     -0.584      0.559      -4.526       2.447
energy:playlist_subgenre[T.dance pop]                                                                              0.4751      1.752      0.271      0.786      -2.958       3.909
energy:playlist_subgenre[T.electro house]                                                                          1.4172      1.785      0.794      0.427      -2.082       4.916
energy:playlist_subgenre[T.electropop]                                                                             3.0472      1.735      1.756      0.079      -0.353       6.448
energy:playlist_subgenre[T.gangster rap]                                                                           1.5859      1.783      0.889      0.374      -1.910       5.082
energy:playlist_subgenre[T.hard rock]                                                                              0.4531      1.988      0.228      0.820      -3.444       4.351
energy:playlist_subgenre[T.hip hop]                                                                                0.4607      1.872      0.246      0.806      -3.209       4.131
energy:playlist_subgenre[T.hip pop]                                                                                2.2222      2.140      1.038      0.299      -1.972       6.417
energy:playlist_subgenre[T.indie poptimism]                                                                       -1.6401      1.753     -0.936      0.349      -5.076       1.795
energy:playlist_subgenre[T.latin hip hop]                                                                          2.4768      1.779      1.393      0.164      -1.009       5.963
energy:playlist_subgenre[T.latin pop]                                                                             -0.4917      1.868     -0.263      0.792      -4.153       3.170
energy:playlist_subgenre[T.neo soul]                                                                              -0.6746      1.851     -0.365      0.715      -4.302       2.953
energy:playlist_subgenre[T.new jack swing]                                                                         0.9488      1.854      0.512      0.609      -2.684       4.582
energy:playlist_subgenre[T.permanent wave]                                                                         1.2495      1.864      0.670      0.503      -2.403       4.902
energy:playlist_subgenre[T.pop edm]                                                                                1.9153      2.007      0.955      0.340      -2.018       5.848
energy:playlist_subgenre[T.post-teen pop]                                                                          0.7337      1.854      0.396      0.692      -2.899       4.367
energy:playlist_subgenre[T.progressive electro house]                                                              2.4263      2.299      1.055      0.291      -2.079       6.932
energy:playlist_subgenre[T.reggaeton]                                                                             -2.6866      3.094     -0.868      0.385      -8.750       3.377
energy:playlist_subgenre[T.southern hip hop]                                                                       0.6185      1.702      0.363      0.716      -2.717       3.954
energy:playlist_subgenre[T.trap]                                                                                   3.6304      1.801      2.016      0.044       0.101       7.160
energy:playlist_subgenre[T.tropical]                                                                               0.2173      1.790      0.121      0.903      -3.291       3.726
energy:playlist_subgenre[T.urban contemporary]                                                                    -0.3950      1.940     -0.204      0.839      -4.197       3.407
valence                                                                                                            0.8713      1.631      0.534      0.593      -2.325       4.067
valence:playlist_subgenre[T.big room]                                                                             -3.5346      2.369     -1.492      0.136      -8.178       1.109
valence:playlist_subgenre[T.classic rock]                                                                         -0.7646      2.407     -0.318      0.751      -5.482       3.953
valence:playlist_subgenre[T.dance pop]                                                                             1.6536      2.147      0.770      0.441      -2.554       5.861
valence:playlist_subgenre[T.electro house]                                                                         0.8359      2.067      0.404      0.686      -3.216       4.888
valence:playlist_subgenre[T.electropop]                                                                           -1.1062      2.161     -0.512      0.609      -5.342       3.130
valence:playlist_subgenre[T.gangster rap]                                                                         -0.6984      2.131     -0.328      0.743      -4.876       3.479
valence:playlist_subgenre[T.hard rock]                                                                            -2.9810      2.210     -1.349      0.177      -7.312       1.350
valence:playlist_subgenre[T.hip hop]                                                                              -4.3700      2.154     -2.029      0.043      -8.592      -0.148
valence:playlist_subgenre[T.hip pop]                                                                              -1.7341      2.440     -0.711      0.477      -6.516       3.048
valence:playlist_subgenre[T.indie poptimism]                                                                      -2.1703      2.044     -1.062      0.288      -6.177       1.837
valence:playlist_subgenre[T.latin hip hop]                                                                        -1.6426      2.352     -0.699      0.485      -6.252       2.967
valence:playlist_subgenre[T.latin pop]                                                                            -1.9653      2.459     -0.799      0.424      -6.785       2.854
valence:playlist_subgenre[T.neo soul]                                                                              0.7242      2.110      0.343      0.731      -3.411       4.860
valence:playlist_subgenre[T.new jack swing]                                                                       -4.6102      2.660     -1.733      0.083      -9.823       0.603
valence:playlist_subgenre[T.permanent wave]                                                                       -1.3050      2.364     -0.552      0.581      -5.938       3.328
valence:playlist_subgenre[T.pop edm]                                                                              -2.9871      2.268     -1.317      0.188      -7.433       1.459
valence:playlist_subgenre[T.post-teen pop]                                                                        -1.0227      2.376     -0.430      0.667      -5.680       3.635
valence:playlist_subgenre[T.progressive electro house]                                                             0.0926      2.068      0.045      0.964      -3.961       4.147
valence:playlist_subgenre[T.reggaeton]                                                                             2.7934      3.267      0.855      0.393      -3.610       9.197
valence:playlist_subgenre[T.southern hip hop]                                                                     -0.9877      2.109     -0.468      0.639      -5.121       3.145
valence:playlist_subgenre[T.trap]                                                                                 -2.5715      2.158     -1.192      0.233      -6.801       1.657
valence:playlist_subgenre[T.tropical]                                                                              3.0705      2.193      1.400      0.161      -1.227       7.368
valence:playlist_subgenre[T.urban contemporary]                                                                   -1.0009      2.188     -0.458      0.647      -5.289       3.287
tempo                                                                                                             -0.6311      0.854     -0.739      0.460      -2.305       1.043
tempo:playlist_subgenre[T.big room]                                                                                0.9117      2.933      0.311      0.756      -4.838       6.661
tempo:playlist_subgenre[T.classic rock]                                                                            1.3449      1.370      0.982      0.326      -1.340       4.030
tempo:playlist_subgenre[T.dance pop]                                                                               1.4217      1.409      1.009      0.313      -1.340       4.184
tempo:playlist_subgenre[T.electro house]                                                                           1.2181      2.193      0.555      0.579      -3.080       5.516
tempo:playlist_subgenre[T.electropop]                                                                              1.0378      1.487      0.698      0.485      -1.878       3.953
tempo:playlist_subgenre[T.gangster rap]                                                                            1.6847      1.308      1.288      0.198      -0.880       4.249
tempo:playlist_subgenre[T.hard rock]                                                                               2.3843      1.500      1.589      0.112      -0.556       5.325
tempo:playlist_subgenre[T.hip hop]                                                                                 0.6379      1.128      0.566      0.572      -1.573       2.849
tempo:playlist_subgenre[T.hip pop]                                                                                -0.9121      1.452     -0.628      0.530      -3.759       1.935
tempo:playlist_subgenre[T.indie poptimism]                                                                         1.9054      1.320      1.443      0.149      -0.683       4.494
tempo:playlist_subgenre[T.latin hip hop]                                                                           1.1509      1.421      0.810      0.418      -1.633       3.935
tempo:playlist_subgenre[T.latin pop]                                                                               1.4169      1.528      0.927      0.354      -1.579       4.412
tempo:playlist_subgenre[T.neo soul]                                                                                0.9190      1.182      0.778      0.437      -1.397       3.235
tempo:playlist_subgenre[T.new jack swing]                                                                         -1.2659      1.824     -0.694      0.488      -4.842       2.310
tempo:playlist_subgenre[T.permanent wave]                                                                          0.7511      1.371      0.548      0.584      -1.936       3.438
tempo:playlist_subgenre[T.pop edm]                                                                                 1.5442      1.648      0.937      0.349      -1.687       4.775
tempo:playlist_subgenre[T.post-teen pop]                                                                          -0.2180      1.543     -0.141      0.888      -3.243       2.807
tempo:playlist_subgenre[T.progressive electro house]                                                               2.2390      2.463      0.909      0.363      -2.588       7.066
tempo:playlist_subgenre[T.reggaeton]                                                                               4.7047      2.349      2.003      0.045       0.101       9.309
tempo:playlist_subgenre[T.southern hip hop]                                                                        0.2863      1.225      0.234      0.815      -2.114       2.687
tempo:playlist_subgenre[T.trap]                                                                                   -0.8195      1.667     -0.492      0.623      -4.087       2.448
tempo:playlist_subgenre[T.tropical]                                                                                2.3805      1.606      1.482      0.138      -0.767       5.528
tempo:playlist_subgenre[T.urban contemporary]                                                                      0.0919      1.385      0.066      0.947      -2.622       2.806
duration_ms                                                                                                       -0.6693      0.874     -0.766      0.444      -2.382       1.044
duration_ms:playlist_subgenre[T.big room]                                                                          0.1305      1.809      0.072      0.943      -3.416       3.676
duration_ms:playlist_subgenre[T.classic rock]                                                                      0.6031      1.379      0.437      0.662      -2.099       3.305
duration_ms:playlist_subgenre[T.dance pop]                                                                         0.5880      1.553      0.379      0.705      -2.456       3.632
duration_ms:playlist_subgenre[T.electro house]                                                                    -0.6474      1.082     -0.598      0.550      -2.769       1.474
duration_ms:playlist_subgenre[T.electropop]                                                                       -1.3620      1.377     -0.989      0.323      -4.061       1.337
duration_ms:playlist_subgenre[T.gangster rap]                                                                      1.1770      1.231      0.956      0.339      -1.236       3.590
duration_ms:playlist_subgenre[T.hard rock]                                                                         0.7785      1.381      0.564      0.573      -1.929       3.486
duration_ms:playlist_subgenre[T.hip hop]                                                                           2.8626      1.298      2.205      0.027       0.318       5.407
duration_ms:playlist_subgenre[T.hip pop]                                                                           0.7141      1.397      0.511      0.609      -2.024       3.452
duration_ms:playlist_subgenre[T.indie poptimism]                                                                   1.8921      1.442      1.313      0.189      -0.933       4.718
duration_ms:playlist_subgenre[T.latin hip hop]                                                                     1.2790      1.256      1.018      0.309      -1.183       3.741
duration_ms:playlist_subgenre[T.latin pop]                                                                         0.4343      1.451      0.299      0.765      -2.409       3.277
duration_ms:playlist_subgenre[T.neo soul]                                                                          1.9046      1.224      1.556      0.120      -0.495       4.304
duration_ms:playlist_subgenre[T.new jack swing]                                                                    4.4554      1.990      2.238      0.025       0.554       8.357
duration_ms:playlist_subgenre[T.permanent wave]                                                                   -0.1758      1.518     -0.116      0.908      -3.151       2.799
duration_ms:playlist_subgenre[T.pop edm]                                                                           0.4297      1.669      0.258      0.797      -2.841       3.701
duration_ms:playlist_subgenre[T.post-teen pop]                                                                     2.4348      1.489      1.635      0.102      -0.484       5.353
duration_ms:playlist_subgenre[T.progressive electro house]                                                        -1.0840      1.332     -0.814      0.416      -3.694       1.526
duration_ms:playlist_subgenre[T.reggaeton]                                                                         0.3219      1.786      0.180      0.857      -3.178       3.822
duration_ms:playlist_subgenre[T.southern hip hop]                                                                  1.8038      1.072      1.682      0.093      -0.298       3.906
duration_ms:playlist_subgenre[T.trap]                                                                             -0.3950      1.457     -0.271      0.786      -3.250       2.460
duration_ms:playlist_subgenre[T.tropical]                                                                          0.9455      1.319      0.717      0.474      -1.641       3.532
duration_ms:playlist_subgenre[T.urban contemporary]                                                                2.4620      1.268      1.942      0.052      -0.022       4.947
artist_hit_rate                                                                                                   -2.8636      2.476     -1.156      0.248      -7.717       1.990
artist_hit_rate:playlist_subgenre[T.big room]                                                                     -3.5974      6.731     -0.534      0.593     -16.791       9.596
artist_hit_rate:playlist_subgenre[T.classic rock]                                                                  5.9893      3.221      1.859      0.063      -0.324      12.303
artist_hit_rate:playlist_subgenre[T.dance pop]                                                                     2.2421      3.032      0.740      0.460      -3.700       8.184
artist_hit_rate:playlist_subgenre[T.electro house]                                                               -10.3121      5.468     -1.886      0.059     -21.030       0.406
artist_hit_rate:playlist_subgenre[T.electropop]                                                                   -3.5969      2.992     -1.202      0.229      -9.461       2.268
artist_hit_rate:playlist_subgenre[T.gangster rap]                                                                 -1.7299      3.152     -0.549      0.583      -7.907       4.447
artist_hit_rate:playlist_subgenre[T.hard rock]                                                                    -2.7110      3.322     -0.816      0.414      -9.223       3.801
artist_hit_rate:playlist_subgenre[T.hip hop]                                                                       4.3098      3.181      1.355      0.175      -1.925      10.545
artist_hit_rate:playlist_subgenre[T.hip pop]                                                                       5.1269      3.606      1.422      0.155      -1.941      12.195
artist_hit_rate:playlist_subgenre[T.indie poptimism]                                                               4.3791      3.097      1.414      0.157      -1.691      10.449
artist_hit_rate:playlist_subgenre[T.latin hip hop]                                                                 0.4215      3.154      0.134      0.894      -5.761       6.604
artist_hit_rate:playlist_subgenre[T.latin pop]                                                                     2.6037      3.040      0.856      0.392      -3.355       8.563
artist_hit_rate:playlist_subgenre[T.neo soul]                                                                     -1.4755      3.629     -0.407      0.684      -8.589       5.638
artist_hit_rate:playlist_subgenre[T.new jack swing]                                                                3.0457     11.189      0.272      0.785     -18.885      24.977
artist_hit_rate:playlist_subgenre[T.permanent wave]                                                                5.6969      3.112      1.830      0.067      -0.404      11.797
artist_hit_rate:playlist_subgenre[T.pop edm]                                                                      -1.7100      3.287     -0.520      0.603      -8.152       4.733
artist_hit_rate:playlist_subgenre[T.post-teen pop]                                                                 8.1730      3.062      2.669      0.008       2.171      14.175
artist_hit_rate:playlist_subgenre[T.progressive electro house]                                                    -0.3340      5.518     -0.061      0.952     -11.149      10.481
artist_hit_rate:playlist_subgenre[T.reggaeton]                                                                    -0.9779      3.438     -0.284      0.776      -7.716       5.760
artist_hit_rate:playlist_subgenre[T.southern hip hop]                                                             -5.7172      3.613     -1.582      0.114     -12.799       1.365
artist_hit_rate:playlist_subgenre[T.trap]                                                                          1.2831      3.166      0.405      0.685      -4.923       7.490
artist_hit_rate:playlist_subgenre[T.tropical]                                                                      5.5766      3.654      1.526      0.127      -1.585      12.738
artist_hit_rate:playlist_subgenre[T.urban contemporary]                                                            1.7476      3.036      0.576      0.565      -4.203       7.698
artist_n_tracks                                                                                                    4.8597      1.893      2.567      0.010       1.149       8.571
artist_n_tracks:playlist_subgenre[T.big room]                                                                      0.4271      2.592      0.165      0.869      -4.654       5.508
artist_n_tracks:playlist_subgenre[T.classic rock]                                                                 -1.8724      2.599     -0.721      0.471      -6.966       3.221
artist_n_tracks:playlist_subgenre[T.dance pop]                                                                     0.8600      2.474      0.348      0.728      -3.989       5.709
artist_n_tracks:playlist_subgenre[T.electro house]                                                                -4.4776      2.380     -1.882      0.060      -9.142       0.186
artist_n_tracks:playlist_subgenre[T.electropop]                                                                   -5.9169      2.491     -2.375      0.018     -10.799      -1.034
artist_n_tracks:playlist_subgenre[T.gangster rap]                                                                 -5.0327      2.452     -2.053      0.040      -9.838      -0.227
artist_n_tracks:playlist_subgenre[T.hard rock]                                                                    -4.1872      2.516     -1.664      0.096      -9.118       0.744
artist_n_tracks:playlist_subgenre[T.hip hop]                                                                      -2.9106      2.680     -1.086      0.277      -8.163       2.342
artist_n_tracks:playlist_subgenre[T.hip pop]                                                                      -0.1115      3.130     -0.036      0.972      -6.246       6.023
artist_n_tracks:playlist_subgenre[T.indie poptimism]                                                              -6.6103      2.511     -2.632      0.008     -11.533      -1.688
artist_n_tracks:playlist_subgenre[T.latin hip hop]                                                               -10.0671      2.553     -3.944      0.000     -15.070      -5.064
artist_n_tracks:playlist_subgenre[T.latin pop]                                                                    -2.4894      2.660     -0.936      0.349      -7.703       2.724
artist_n_tracks:playlist_subgenre[T.neo soul]                                                                     -4.1265      2.582     -1.598      0.110      -9.187       0.934
artist_n_tracks:playlist_subgenre[T.new jack swing]                                                               -3.4107      2.744     -1.243      0.214      -8.789       1.967
artist_n_tracks:playlist_subgenre[T.permanent wave]                                                               -3.9590      2.692     -1.471      0.141      -9.236       1.318
artist_n_tracks:playlist_subgenre[T.pop edm]                                                                      -7.3842      2.644     -2.792      0.005     -12.567      -2.201
artist_n_tracks:playlist_subgenre[T.post-teen pop]                                                                -3.7995      2.577     -1.474      0.140      -8.851       1.252
artist_n_tracks:playlist_subgenre[T.progressive electro house]                                                    -7.6105      2.379     -3.199      0.001     -12.274      -2.947
artist_n_tracks:playlist_subgenre[T.reggaeton]                                                                    -2.1574      2.908     -0.742      0.458      -7.857       3.542
artist_n_tracks:playlist_subgenre[T.southern hip hop]                                                             -2.6867      2.327     -1.155      0.248      -7.247       1.874
artist_n_tracks:playlist_subgenre[T.trap]                                                                         -2.3264      2.762     -0.842      0.400      -7.741       3.088
artist_n_tracks:playlist_subgenre[T.tropical]                                                                     -3.2632      2.812     -1.160      0.246      -8.776       2.249
artist_n_tracks:playlist_subgenre[T.urban contemporary]                                                           -2.2096      2.483     -0.890      0.374      -7.077       2.658
I(artist_avg_popularity ** 2)                                                                                      5.5397      2.046      2.707      0.007       1.529       9.551
I(artist_avg_popularity ** 2):playlist_subgenre[T.big room]                                                        6.3250      3.610      1.752      0.080      -0.751      13.401
I(artist_avg_popularity ** 2):playlist_subgenre[T.classic rock]                                                    2.8588      2.717      1.052      0.293      -2.466       8.184
I(artist_avg_popularity ** 2):playlist_subgenre[T.dance pop]                                                      -0.5825      3.029     -0.192      0.847      -6.519       5.354
I(artist_avg_popularity ** 2):playlist_subgenre[T.electro house]                                                   8.1731      2.989      2.734      0.006       2.314      14.032
I(artist_avg_popularity ** 2):playlist_subgenre[T.electropop]                                                      6.2772      2.713      2.314      0.021       0.960      11.594
I(artist_avg_popularity ** 2):playlist_subgenre[T.gangster rap]                                                    8.4024      2.780      3.022      0.003       2.953      13.852
I(artist_avg_popularity ** 2):playlist_subgenre[T.hard rock]                                                       7.5232      2.725      2.761      0.006       2.182      12.865
I(artist_avg_popularity ** 2):playlist_subgenre[T.hip hop]                                                        -0.3300      4.110     -0.080      0.936      -8.386       7.726
I(artist_avg_popularity ** 2):playlist_subgenre[T.hip pop]                                                         1.4659      2.892      0.507      0.612      -4.203       7.134
I(artist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism]                                                 4.5982      2.485      1.851      0.064      -0.272       9.468
I(artist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop]                                                   3.8441      2.710      1.419      0.156      -1.467       9.155
I(artist_avg_popularity ** 2):playlist_subgenre[T.latin pop]                                                       3.3312      3.090      1.078      0.281      -2.725       9.387
I(artist_avg_popularity ** 2):playlist_subgenre[T.neo soul]                                                        3.3444      2.630      1.272      0.204      -1.811       8.500
I(artist_avg_popularity ** 2):playlist_subgenre[T.new jack swing]                                                 10.6749      3.986      2.678      0.007       2.862      18.487
I(artist_avg_popularity ** 2):playlist_subgenre[T.permanent wave]                                                 -1.2941      2.935     -0.441      0.659      -7.047       4.459
I(artist_avg_popularity ** 2):playlist_subgenre[T.pop edm]                                                         4.1253      3.251      1.269      0.205      -2.247      10.498
I(artist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop]                                                   0.2328      2.970      0.078      0.938      -5.589       6.055
I(artist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house]                                       8.1164      3.192      2.543      0.011       1.860      14.373
I(artist_avg_popularity ** 2):playlist_subgenre[T.reggaeton]                                                       5.4154      6.809      0.795      0.426      -7.930      18.761
I(artist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop]                                                4.5167      2.623      1.722      0.085      -0.624       9.657
I(artist_avg_popularity ** 2):playlist_subgenre[T.trap]                                                            0.4838      3.619      0.134      0.894      -6.610       7.578
I(artist_avg_popularity ** 2):playlist_subgenre[T.tropical]                                                        5.0096      2.892      1.733      0.083      -0.658      10.677
I(artist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary]                                              3.8436      2.836      1.355      0.175      -1.715       9.403
I(playlist_avg_popularity ** 2)                                                                                    5.2288      3.497      1.495      0.135      -1.626      12.084
I(playlist_avg_popularity ** 2):playlist_subgenre[T.big room]                                                      3.7906      7.494      0.506      0.613     -10.898      18.479
I(playlist_avg_popularity ** 2):playlist_subgenre[T.classic rock]                                                 -4.8690      5.395     -0.902      0.367     -15.444       5.706
I(playlist_avg_popularity ** 2):playlist_subgenre[T.dance pop]                                                    26.1758     37.709      0.694      0.488     -47.737     100.088
I(playlist_avg_popularity ** 2):playlist_subgenre[T.electro house]                                                -3.9510      5.278     -0.749      0.454     -14.296       6.394
I(playlist_avg_popularity ** 2):playlist_subgenre[T.electropop]                                                   -1.9524      4.633     -0.421      0.673     -11.034       7.129
I(playlist_avg_popularity ** 2):playlist_subgenre[T.gangster rap]                                                 10.9005      5.351      2.037      0.042       0.413      21.388
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hard rock]                                                    -1.0139      5.313     -0.191      0.849     -11.427       9.400
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip hop]                                                     838.8790    430.775      1.947      0.052      -5.463    1683.221
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip pop]                                                      17.4270     11.418      1.526      0.127      -4.953      39.807
I(playlist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism]                                              -8.6410      4.947     -1.747      0.081     -18.338       1.056
I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop]                                                -0.2836      4.199     -0.068      0.946      -8.514       7.947
I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin pop]                                                     7.8441      8.771      0.894      0.371      -9.348      25.037
I(playlist_avg_popularity ** 2):playlist_subgenre[T.neo soul]                                                     -8.4147      4.655     -1.808      0.071     -17.538       0.709
I(playlist_avg_popularity ** 2):playlist_subgenre[T.new jack swing]                                                1.0754      7.320      0.147      0.883     -13.271      15.422
I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave]                                              -96.9527     20.161     -4.809      0.000    -136.470     -57.436
I(playlist_avg_popularity ** 2):playlist_subgenre[T.pop edm]                                                       7.4560      5.027      1.483      0.138      -2.397      17.309
I(playlist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop]                                               -85.2748     28.468     -2.995      0.003    -141.074     -29.476
I(playlist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house]                                     2.2438      7.292      0.308      0.758     -12.049      16.536
I(playlist_avg_popularity ** 2):playlist_subgenre[T.reggaeton]                                                    -0.0971      7.836     -0.012      0.990     -15.456      15.261
I(playlist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop]                                              8.9136      7.193      1.239      0.215      -5.185      23.013
I(playlist_avg_popularity ** 2):playlist_subgenre[T.trap]                                                        -18.8118     10.351     -1.817      0.069     -39.099       1.476
I(playlist_avg_popularity ** 2):playlist_subgenre[T.tropical]                                                    -26.6551     17.260     -1.544      0.123     -60.485       7.175
I(playlist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary]                                           -0.7837      6.252     -0.125      0.900     -13.038      11.470
I(danceability ** 2)                                                                                               0.4451      1.343      0.331      0.740      -2.187       3.077
I(danceability ** 2):playlist_subgenre[T.big room]                                                                 1.2908      2.113      0.611      0.541      -2.850       5.432
I(danceability ** 2):playlist_subgenre[T.classic rock]                                                             2.7956      1.915      1.460      0.144      -0.957       6.548
I(danceability ** 2):playlist_subgenre[T.dance pop]                                                               -0.9468      1.955     -0.484      0.628      -4.779       2.885
I(danceability ** 2):playlist_subgenre[T.electro house]                                                           -0.1231      1.789     -0.069      0.945      -3.629       3.383
I(danceability ** 2):playlist_subgenre[T.electropop]                                                               0.4802      1.769      0.271      0.786      -2.988       3.949
I(danceability ** 2):playlist_subgenre[T.gangster rap]                                                            -0.4261      1.847     -0.231      0.818      -4.047       3.195
I(danceability ** 2):playlist_subgenre[T.hard rock]                                                                0.2264      2.010      0.113      0.910      -3.713       4.166
I(danceability ** 2):playlist_subgenre[T.hip hop]                                                                 -0.7394      1.831     -0.404      0.686      -4.329       2.850
I(danceability ** 2):playlist_subgenre[T.hip pop]                                                                  1.4095      2.164      0.651      0.515      -2.832       5.651
I(danceability ** 2):playlist_subgenre[T.indie poptimism]                                                         -1.6100      1.726     -0.933      0.351      -4.992       1.772
I(danceability ** 2):playlist_subgenre[T.latin hip hop]                                                           -1.8534      1.965     -0.943      0.345      -5.704       1.997
I(danceability ** 2):playlist_subgenre[T.latin pop]                                                                0.9238      2.040      0.453      0.651      -3.076       4.923
I(danceability ** 2):playlist_subgenre[T.neo soul]                                                                -0.7533      1.776     -0.424      0.671      -4.233       2.727
I(danceability ** 2):playlist_subgenre[T.new jack swing]                                                          -2.0662      2.169     -0.952      0.341      -6.318       2.186
I(danceability ** 2):playlist_subgenre[T.permanent wave]                                                           0.7022      1.993      0.352      0.725      -3.204       4.608
I(danceability ** 2):playlist_subgenre[T.pop edm]                                                                 -1.2356      2.153     -0.574      0.566      -5.457       2.985
I(danceability ** 2):playlist_subgenre[T.post-teen pop]                                                           -0.3384      2.027     -0.167      0.867      -4.311       3.634
I(danceability ** 2):playlist_subgenre[T.progressive electro house]                                               -1.5256      1.860     -0.820      0.412      -5.172       2.120
I(danceability ** 2):playlist_subgenre[T.reggaeton]                                                               -4.7943      3.262     -1.470      0.142     -11.188       1.600
I(danceability ** 2):playlist_subgenre[T.southern hip hop]                                                         0.3173      1.684      0.188      0.851      -2.984       3.619
I(danceability ** 2):playlist_subgenre[T.trap]                                                                     2.7282      1.855      1.470      0.141      -0.909       6.365
I(danceability ** 2):playlist_subgenre[T.tropical]                                                                -1.0741      1.874     -0.573      0.566      -4.747       2.599
I(danceability ** 2):playlist_subgenre[T.urban contemporary]                                                      -0.8839      1.771     -0.499      0.618      -4.355       2.587
I(energy ** 2)                                                                                                     0.9060      1.217      0.744      0.457      -1.480       3.292
I(energy ** 2):playlist_subgenre[T.big room]                                                                      -1.5423      2.939     -0.525      0.600      -7.303       4.219
I(energy ** 2):playlist_subgenre[T.classic rock]                                                                   1.0782      2.089      0.516      0.606      -3.017       5.173
I(energy ** 2):playlist_subgenre[T.dance pop]                                                                     -4.2859      2.045     -2.096      0.036      -8.294      -0.278
I(energy ** 2):playlist_subgenre[T.electro house]                                                                 -1.0551      2.105     -0.501      0.616      -5.182       3.071
I(energy ** 2):playlist_subgenre[T.electropop]                                                                     1.8698      1.895      0.987      0.324      -1.845       5.584
I(energy ** 2):playlist_subgenre[T.gangster rap]                                                                  -4.4047      2.216     -1.987      0.047      -8.749      -0.061
I(energy ** 2):playlist_subgenre[T.hard rock]                                                                     -3.6187      2.395     -1.511      0.131      -8.313       1.076
I(energy ** 2):playlist_subgenre[T.hip hop]                                                                       -0.9969      1.577     -0.632      0.527      -4.088       2.095
I(energy ** 2):playlist_subgenre[T.hip pop]                                                                        0.1497      2.009      0.075      0.941      -3.787       4.087
I(energy ** 2):playlist_subgenre[T.indie poptimism]                                                               -1.7426      1.560     -1.117      0.264      -4.799       1.314
I(energy ** 2):playlist_subgenre[T.latin hip hop]                                                                  0.5418      2.211      0.245      0.806      -3.792       4.876
I(energy ** 2):playlist_subgenre[T.latin pop]                                                                     -3.3578      1.805     -1.861      0.063      -6.895       0.180
I(energy ** 2):playlist_subgenre[T.neo soul]                                                                      -0.3453      1.596     -0.216      0.829      -3.473       2.782
I(energy ** 2):playlist_subgenre[T.new jack swing]                                                                -2.9113      2.006     -1.451      0.147      -6.844       1.021
I(energy ** 2):playlist_subgenre[T.permanent wave]                                                                -1.7455      1.732     -1.008      0.313      -5.139       1.648
I(energy ** 2):playlist_subgenre[T.pop edm]                                                                       -1.2829      2.677     -0.479      0.632      -6.530       3.964
I(energy ** 2):playlist_subgenre[T.post-teen pop]                                                                 -2.0306      1.862     -1.090      0.276      -5.681       1.619
I(energy ** 2):playlist_subgenre[T.progressive electro house]                                                     -2.6110      2.331     -1.120      0.263      -7.181       1.959
I(energy ** 2):playlist_subgenre[T.reggaeton]                                                                      4.0493      3.717      1.089      0.276      -3.236      11.335
I(energy ** 2):playlist_subgenre[T.southern hip hop]                                                              -4.3845      2.140     -2.049      0.041      -8.579      -0.190
I(energy ** 2):playlist_subgenre[T.trap]                                                                          -1.6329      2.249     -0.726      0.468      -6.041       2.775
I(energy ** 2):playlist_subgenre[T.tropical]                                                                      -1.2259      1.697     -0.723      0.470      -4.551       2.100
I(energy ** 2):playlist_subgenre[T.urban contemporary]                                                             0.1291      1.572      0.082      0.935      -2.951       3.210
I(valence ** 2)                                                                                                   -0.2305      1.599     -0.144      0.885      -3.364       2.903
I(valence ** 2):playlist_subgenre[T.big room]                                                                     -1.5195      3.119     -0.487      0.626      -7.633       4.594
I(valence ** 2):playlist_subgenre[T.classic rock]                                                                  1.7124      2.191      0.781      0.435      -2.583       6.007
I(valence ** 2):playlist_subgenre[T.dance pop]                                                                    -0.5040      2.180     -0.231      0.817      -4.778       3.770
I(valence ** 2):playlist_subgenre[T.electro house]                                                                -1.2812      2.238     -0.573      0.567      -5.667       3.105
I(valence ** 2):playlist_subgenre[T.electropop]                                                                    0.3732      2.156      0.173      0.863      -3.852       4.599
I(valence ** 2):playlist_subgenre[T.gangster rap]                                                                 -3.1950      2.211     -1.445      0.148      -7.529       1.139
I(valence ** 2):playlist_subgenre[T.hard rock]                                                                     0.8121      2.339      0.347      0.728      -3.772       5.396
I(valence ** 2):playlist_subgenre[T.hip hop]                                                                       1.5009      2.180      0.688      0.491      -2.772       5.774
I(valence ** 2):playlist_subgenre[T.hip pop]                                                                      -0.6172      2.456     -0.251      0.802      -5.430       4.196
I(valence ** 2):playlist_subgenre[T.indie poptimism]                                                              -0.7184      2.178     -0.330      0.742      -4.988       3.551
I(valence ** 2):playlist_subgenre[T.latin hip hop]                                                                 1.8771      2.164      0.867      0.386      -2.365       6.119
I(valence ** 2):playlist_subgenre[T.latin pop]                                                                     0.5438      2.179      0.250      0.803      -3.726       4.814
I(valence ** 2):playlist_subgenre[T.neo soul]                                                                      1.3429      2.099      0.640      0.522      -2.771       5.457
I(valence ** 2):playlist_subgenre[T.new jack swing]                                                                1.0193      2.419      0.421      0.674      -3.723       5.761
I(valence ** 2):playlist_subgenre[T.permanent wave]                                                                1.8104      2.270      0.798      0.425      -2.639       6.260
I(valence ** 2):playlist_subgenre[T.pop edm]                                                                       1.2543      2.403      0.522      0.602      -3.456       5.964
I(valence ** 2):playlist_subgenre[T.post-teen pop]                                                                 0.1665      2.259      0.074      0.941      -4.262       4.595
I(valence ** 2):playlist_subgenre[T.progressive electro house]                                                    -0.3411      2.245     -0.152      0.879      -4.741       4.059
I(valence ** 2):playlist_subgenre[T.reggaeton]                                                                     6.4864      3.379      1.919      0.055      -0.137      13.110
I(valence ** 2):playlist_subgenre[T.southern hip hop]                                                              0.5741      2.069      0.278      0.781      -3.481       4.629
I(valence ** 2):playlist_subgenre[T.trap]                                                                         -1.8127      2.340     -0.775      0.439      -6.399       2.774
I(valence ** 2):playlist_subgenre[T.tropical]                                                                     -1.1656      2.188     -0.533      0.594      -5.454       3.123
I(valence ** 2):playlist_subgenre[T.urban contemporary]                                                            1.7956      2.219      0.809      0.418      -2.554       6.145
I(tempo ** 2)                                                                                                     -0.5728      0.885     -0.647      0.518      -2.307       1.162
I(tempo ** 2):playlist_subgenre[T.big room]                                                                        0.5618      2.329      0.241      0.809      -4.003       5.127
I(tempo ** 2):playlist_subgenre[T.classic rock]                                                                   -0.3017      1.282     -0.235      0.814      -2.815       2.211
I(tempo ** 2):playlist_subgenre[T.dance pop]                                                                       1.3954      1.426      0.979      0.328      -1.400       4.190
I(tempo ** 2):playlist_subgenre[T.electro house]                                                                   1.2654      1.934      0.654      0.513      -2.526       5.056
I(tempo ** 2):playlist_subgenre[T.electropop]                                                                      1.4500      1.353      1.072      0.284      -1.201       4.101
I(tempo ** 2):playlist_subgenre[T.gangster rap]                                                                    0.5893      1.287      0.458      0.647      -1.933       3.111
I(tempo ** 2):playlist_subgenre[T.hard rock]                                                                       1.9941      1.347      1.480      0.139      -0.646       4.635
I(tempo ** 2):playlist_subgenre[T.hip hop]                                                                         0.3335      1.215      0.275      0.784      -2.048       2.715
I(tempo ** 2):playlist_subgenre[T.hip pop]                                                                         1.3406      1.402      0.956      0.339      -1.407       4.088
I(tempo ** 2):playlist_subgenre[T.indie poptimism]                                                                -1.6395      1.214     -1.350      0.177      -4.019       0.740
I(tempo ** 2):playlist_subgenre[T.latin hip hop]                                                                  -0.5371      1.157     -0.464      0.642      -2.805       1.730
I(tempo ** 2):playlist_subgenre[T.latin pop]                                                                       1.8861      1.307      1.443      0.149      -0.675       4.447
I(tempo ** 2):playlist_subgenre[T.neo soul]                                                                        0.9525      1.193      0.798      0.425      -1.387       3.292
I(tempo ** 2):playlist_subgenre[T.new jack swing]                                                                  0.6557      1.389      0.472      0.637      -2.067       3.378
I(tempo ** 2):playlist_subgenre[T.permanent wave]                                                                  1.5071      1.308      1.152      0.249      -1.057       4.071
I(tempo ** 2):playlist_subgenre[T.pop edm]                                                                        -0.7182      1.464     -0.491      0.624      -3.587       2.151
I(tempo ** 2):playlist_subgenre[T.post-teen pop]                                                                   3.4179      1.348      2.536      0.011       0.776       6.060
I(tempo ** 2):playlist_subgenre[T.progressive electro house]                                                       2.4131      2.751      0.877      0.380      -2.979       7.805
I(tempo ** 2):playlist_subgenre[T.reggaeton]                                                                      -1.3634      1.606     -0.849      0.396      -4.511       1.784
I(tempo ** 2):playlist_subgenre[T.southern hip hop]                                                               -1.4826      1.196     -1.239      0.215      -3.827       0.862
I(tempo ** 2):playlist_subgenre[T.trap]                                                                            1.6059      1.566      1.026      0.305      -1.463       4.675
I(tempo ** 2):playlist_subgenre[T.tropical]                                                                       -0.5996      1.481     -0.405      0.686      -3.502       2.303
I(tempo ** 2):playlist_subgenre[T.urban contemporary]                                                             -0.3965      1.241     -0.320      0.749      -2.828       2.035
I(duration_ms ** 2)                                                                                                0.2105      0.608      0.346      0.729      -0.981       1.402
I(duration_ms ** 2):playlist_subgenre[T.big room]                                                                 -1.4170      1.470     -0.964      0.335      -4.298       1.464
I(duration_ms ** 2):playlist_subgenre[T.classic rock]                                                              1.4702      1.133      1.298      0.194      -0.750       3.691
I(duration_ms ** 2):playlist_subgenre[T.dance pop]                                                                -0.2793      1.196     -0.234      0.815      -2.623       2.064
I(duration_ms ** 2):playlist_subgenre[T.electro house]                                                            -0.1904      0.786     -0.242      0.808      -1.730       1.349
I(duration_ms ** 2):playlist_subgenre[T.electropop]                                                               -0.9439      0.948     -0.996      0.319      -2.801       0.914
I(duration_ms ** 2):playlist_subgenre[T.gangster rap]                                                             -0.5102      1.025     -0.498      0.619      -2.518       1.498
I(duration_ms ** 2):playlist_subgenre[T.hard rock]                                                                -0.1488      0.950     -0.157      0.876      -2.012       1.714
I(duration_ms ** 2):playlist_subgenre[T.hip hop]                                                                   0.3458      0.959      0.361      0.718      -1.533       2.225
I(duration_ms ** 2):playlist_subgenre[T.hip pop]                                                                   0.6780      1.276      0.531      0.595      -1.822       3.178
I(duration_ms ** 2):playlist_subgenre[T.indie poptimism]                                                          -1.2139      1.170     -1.038      0.300      -3.507       1.079
I(duration_ms ** 2):playlist_subgenre[T.latin hip hop]                                                             0.2607      0.896      0.291      0.771      -1.496       2.018
I(duration_ms ** 2):playlist_subgenre[T.latin pop]                                                                 0.0472      1.409      0.034      0.973      -2.715       2.810
I(duration_ms ** 2):playlist_subgenre[T.neo soul]                                                                  0.2432      0.845      0.288      0.773      -1.412       1.899
I(duration_ms ** 2):playlist_subgenre[T.new jack swing]                                                           -1.3907      1.303     -1.067      0.286      -3.945       1.163
I(duration_ms ** 2):playlist_subgenre[T.permanent wave]                                                            0.6562      1.307      0.502      0.616      -1.906       3.219
I(duration_ms ** 2):playlist_subgenre[T.pop edm]                                                                  -1.1728      1.350     -0.869      0.385      -3.818       1.473
I(duration_ms ** 2):playlist_subgenre[T.post-teen pop]                                                             1.2663      1.273      0.995      0.320      -1.229       3.761
I(duration_ms ** 2):playlist_subgenre[T.progressive electro house]                                                -0.0040      1.322     -0.003      0.998      -2.594       2.586
I(duration_ms ** 2):playlist_subgenre[T.reggaeton]                                                                 0.0045      1.448      0.003      0.998      -2.833       2.842
I(duration_ms ** 2):playlist_subgenre[T.southern hip hop]                                                          0.6380      0.795      0.802      0.422      -0.920       2.196
I(duration_ms ** 2):playlist_subgenre[T.trap]                                                                      1.1207      1.164      0.963      0.336      -1.160       3.402
I(duration_ms ** 2):playlist_subgenre[T.tropical]                                                                  0.2269      1.049      0.216      0.829      -1.829       2.283
I(duration_ms ** 2):playlist_subgenre[T.urban contemporary]                                                        0.1917      0.911      0.210      0.833      -1.594       1.978
I(artist_hit_rate ** 2)                                                                                           -4.5358      4.825     -0.940      0.347     -13.994       4.922
I(artist_hit_rate ** 2):playlist_subgenre[T.big room]                                                              6.9241      8.504      0.814      0.416      -9.745      23.593
I(artist_hit_rate ** 2):playlist_subgenre[T.classic rock]                                                         13.9855      6.622      2.112      0.035       1.006      26.965
I(artist_hit_rate ** 2):playlist_subgenre[T.dance pop]                                                            -7.2546      6.860     -1.058      0.290     -20.700       6.190
I(artist_hit_rate ** 2):playlist_subgenre[T.electro house]                                                       -15.2051      9.974     -1.524      0.127     -34.754       4.344
I(artist_hit_rate ** 2):playlist_subgenre[T.electropop]                                                            2.3961      6.530      0.367      0.714     -10.403      15.196
I(artist_hit_rate ** 2):playlist_subgenre[T.gangster rap]                                                          5.1983      6.337      0.820      0.412      -7.222      17.618
I(artist_hit_rate ** 2):playlist_subgenre[T.hard rock]                                                            -0.3423      6.756     -0.051      0.960     -13.585      12.900
I(artist_hit_rate ** 2):playlist_subgenre[T.hip hop]                                                               7.8268      7.792      1.004      0.315      -7.447      23.100
I(artist_hit_rate ** 2):playlist_subgenre[T.hip pop]                                                               9.7511      8.907      1.095      0.274      -7.708      27.210
I(artist_hit_rate ** 2):playlist_subgenre[T.indie poptimism]                                                      17.9492      7.530      2.384      0.017       3.190      32.708
I(artist_hit_rate ** 2):playlist_subgenre[T.latin hip hop]                                                         8.8263      7.373      1.197      0.231      -5.625      23.277
I(artist_hit_rate ** 2):playlist_subgenre[T.latin pop]                                                             4.2054      7.200      0.584      0.559      -9.906      18.317
I(artist_hit_rate ** 2):playlist_subgenre[T.neo soul]                                                             13.2709      7.534      1.762      0.078      -1.496      28.038
I(artist_hit_rate ** 2):playlist_subgenre[T.new jack swing]                                                       13.8033     27.535      0.501      0.616     -40.167      67.773
I(artist_hit_rate ** 2):playlist_subgenre[T.permanent wave]                                                      -11.5700      7.456     -1.552      0.121     -26.184       3.044
I(artist_hit_rate ** 2):playlist_subgenre[T.pop edm]                                                              -1.3638      8.004     -0.170      0.865     -17.052      14.325
I(artist_hit_rate ** 2):playlist_subgenre[T.post-teen pop]                                                        -1.1403      6.883     -0.166      0.868     -14.631      12.350
I(artist_hit_rate ** 2):playlist_subgenre[T.progressive electro house]                                            11.5645      7.769      1.488      0.137      -3.664      26.793
I(artist_hit_rate ** 2):playlist_subgenre[T.reggaeton]                                                             5.0538      6.827      0.740      0.459      -8.328      18.435
I(artist_hit_rate ** 2):playlist_subgenre[T.southern hip hop]                                                     -5.2627      6.439     -0.817      0.414     -17.884       7.358
I(artist_hit_rate ** 2):playlist_subgenre[T.trap]                                                                  6.4783      6.937      0.934      0.350      -7.119      20.075
I(artist_hit_rate ** 2):playlist_subgenre[T.tropical]                                                             15.0845      8.334      1.810      0.070      -1.250      31.419
I(artist_hit_rate ** 2):playlist_subgenre[T.urban contemporary]                                                   -2.4634      7.432     -0.331      0.740     -17.030      12.103
I(artist_n_tracks ** 2)                                                                                           -5.8356      2.864     -2.038      0.042     -11.449      -0.223
I(artist_n_tracks ** 2):playlist_subgenre[T.big room]                                                              7.3515      4.331      1.697      0.090      -1.137      15.841
I(artist_n_tracks ** 2):playlist_subgenre[T.classic rock]                                                         13.5498      3.997      3.390      0.001       5.715      21.385
I(artist_n_tracks ** 2):playlist_subgenre[T.dance pop]                                                             5.7474      4.018      1.430      0.153      -2.128      13.622
I(artist_n_tracks ** 2):playlist_subgenre[T.electro house]                                                         6.3692      4.004      1.591      0.112      -1.478      14.217
I(artist_n_tracks ** 2):playlist_subgenre[T.electropop]                                                            4.9822      3.859      1.291      0.197      -2.581      12.545
I(artist_n_tracks ** 2):playlist_subgenre[T.gangster rap]                                                          7.4508      4.242      1.757      0.079      -0.863      15.765
I(artist_n_tracks ** 2):playlist_subgenre[T.hard rock]                                                             3.9961      3.966      1.008      0.314      -3.777      11.769
I(artist_n_tracks ** 2):playlist_subgenre[T.hip hop]                                                               3.3369      4.370      0.764      0.445      -5.229      11.903
I(artist_n_tracks ** 2):playlist_subgenre[T.hip pop]                                                              11.1703      4.972      2.247      0.025       1.425      20.916
I(artist_n_tracks ** 2):playlist_subgenre[T.indie poptimism]                                                       4.9672      4.019      1.236      0.216      -2.910      12.844
I(artist_n_tracks ** 2):playlist_subgenre[T.latin hip hop]                                                         5.4074      4.146      1.304      0.192      -2.719      13.534
I(artist_n_tracks ** 2):playlist_subgenre[T.latin pop]                                                             9.1134      4.388      2.077      0.038       0.513      17.714
I(artist_n_tracks ** 2):playlist_subgenre[T.neo soul]                                                              4.6623      4.240      1.100      0.272      -3.648      12.973
I(artist_n_tracks ** 2):playlist_subgenre[T.new jack swing]                                                        8.0327      5.042      1.593      0.111      -1.851      17.916
I(artist_n_tracks ** 2):playlist_subgenre[T.permanent wave]                                                        4.5126      4.349      1.038      0.299      -4.011      13.036
I(artist_n_tracks ** 2):playlist_subgenre[T.pop edm]                                                              10.8310      4.317      2.509      0.012       2.370      19.292
I(artist_n_tracks ** 2):playlist_subgenre[T.post-teen pop]                                                         5.4403      3.984      1.365      0.172      -2.369      13.250
I(artist_n_tracks ** 2):playlist_subgenre[T.progressive electro house]                                             3.8962      3.935      0.990      0.322      -3.817      11.609
I(artist_n_tracks ** 2):playlist_subgenre[T.reggaeton]                                                             6.6271      5.007      1.324      0.186      -3.186      16.440
I(artist_n_tracks ** 2):playlist_subgenre[T.southern hip hop]                                                      2.3579      3.829      0.616      0.538      -5.148       9.863
I(artist_n_tracks ** 2):playlist_subgenre[T.trap]                                                                  8.4679      4.340      1.951      0.051      -0.038      16.974
I(artist_n_tracks ** 2):playlist_subgenre[T.tropical]                                                              6.0892      4.703      1.295      0.195      -3.129      15.307
I(artist_n_tracks ** 2):playlist_subgenre[T.urban contemporary]                                                    5.9166      4.225      1.400      0.161      -2.364      14.197
I(artist_avg_popularity ** 3)                                                                                      3.9201      1.511      2.594      0.010       0.958       6.883
I(artist_avg_popularity ** 3):playlist_subgenre[T.big room]                                                       -1.9467      2.473     -0.787      0.431      -6.795       2.901
I(artist_avg_popularity ** 3):playlist_subgenre[T.classic rock]                                                    0.4206      2.127      0.198      0.843      -3.749       4.590
I(artist_avg_popularity ** 3):playlist_subgenre[T.dance pop]                                                      -1.9528      1.934     -1.010      0.313      -5.743       1.837
I(artist_avg_popularity ** 3):playlist_subgenre[T.electro house]                                                  -2.5991      2.200     -1.182      0.237      -6.911       1.713
I(artist_avg_popularity ** 3):playlist_subgenre[T.electropop]                                                     -0.1635      1.932     -0.085      0.933      -3.951       3.623
I(artist_avg_popularity ** 3):playlist_subgenre[T.gangster rap]                                                   -0.9812      2.070     -0.474      0.635      -5.038       3.075
I(artist_avg_popularity ** 3):playlist_subgenre[T.hard rock]                                                      -0.2852      2.035     -0.140      0.889      -4.273       3.703
I(artist_avg_popularity ** 3):playlist_subgenre[T.hip hop]                                                        -0.2657      2.000     -0.133      0.894      -4.186       3.655
I(artist_avg_popularity ** 3):playlist_subgenre[T.hip pop]                                                        -3.0710      2.021     -1.520      0.129      -7.032       0.890
I(artist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism]                                                -2.3894      1.828     -1.307      0.191      -5.972       1.193
I(artist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop]                                                  -3.0958      1.938     -1.598      0.110      -6.894       0.702
I(artist_avg_popularity ** 3):playlist_subgenre[T.latin pop]                                                      -4.6036      1.999     -2.303      0.021      -8.522      -0.685
I(artist_avg_popularity ** 3):playlist_subgenre[T.neo soul]                                                       -1.9739      1.860     -1.061      0.289      -5.619       1.671
I(artist_avg_popularity ** 3):playlist_subgenre[T.new jack swing]                                                 -0.8604      2.728     -0.315      0.752      -6.207       4.486
I(artist_avg_popularity ** 3):playlist_subgenre[T.permanent wave]                                                 -6.5769      2.000     -3.289      0.001     -10.497      -2.657
I(artist_avg_popularity ** 3):playlist_subgenre[T.pop edm]                                                        -0.1156      2.228     -0.052      0.959      -4.483       4.251
I(artist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop]                                                  -5.0715      1.899     -2.671      0.008      -8.793      -1.350
I(artist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house]                                      -0.2674      2.127     -0.126      0.900      -4.436       3.901
I(artist_avg_popularity ** 3):playlist_subgenre[T.reggaeton]                                                      -1.2440      3.146     -0.395      0.693      -7.411       4.923
I(artist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop]                                               -2.1137      1.927     -1.097      0.273      -5.890       1.662
I(artist_avg_popularity ** 3):playlist_subgenre[T.trap]                                                           -0.6778      2.138     -0.317      0.751      -4.869       3.513
I(artist_avg_popularity ** 3):playlist_subgenre[T.tropical]                                                       -2.3042      2.067     -1.115      0.265      -6.356       1.747
I(artist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary]                                             -0.4825      1.944     -0.248      0.804      -4.294       3.328
I(playlist_avg_popularity ** 3)                                                                                    0.8439      0.646      1.307      0.191      -0.422       2.110
I(playlist_avg_popularity ** 3):playlist_subgenre[T.big room]                                                     20.3354      9.298      2.187      0.029       2.112      38.559
I(playlist_avg_popularity ** 3):playlist_subgenre[T.classic rock]                                                 -8.1745      3.566     -2.293      0.022     -15.164      -1.185
I(playlist_avg_popularity ** 3):playlist_subgenre[T.dance pop]                                                   -46.1502     42.763     -1.079      0.280    -129.967      37.667
I(playlist_avg_popularity ** 3):playlist_subgenre[T.electro house]                                                 1.5047      1.702      0.884      0.377      -1.832       4.841
I(playlist_avg_popularity ** 3):playlist_subgenre[T.electropop]                                                    0.1956      0.800      0.245      0.807      -1.372       1.763
I(playlist_avg_popularity ** 3):playlist_subgenre[T.gangster rap]                                                  5.0763      2.035      2.494      0.013       1.087       9.066
I(playlist_avg_popularity ** 3):playlist_subgenre[T.hard rock]                                                    -1.0363      1.983     -0.522      0.601      -4.924       2.851
I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip hop]                                                    -523.2436    260.620     -2.008      0.045   -1034.072     -12.416
I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip pop]                                                      -8.3433      7.455     -1.119      0.263     -22.956       6.269
I(playlist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism]                                              -0.1076      4.171     -0.026      0.979      -8.282       8.067
I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop]                                                -0.3871      0.869     -0.446      0.656      -2.090       1.315
I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin pop]                                                     1.1257      2.185      0.515      0.606      -3.156       5.408
I(playlist_avg_popularity ** 3):playlist_subgenre[T.neo soul]                                                      0.1801      1.359      0.132      0.895      -2.484       2.844
I(playlist_avg_popularity ** 3):playlist_subgenre[T.new jack swing]                                                3.2099      8.194      0.392      0.695     -12.851      19.271
I(playlist_avg_popularity ** 3):playlist_subgenre[T.permanent wave]                                              139.1233     40.043      3.474      0.001      60.637     217.610
I(playlist_avg_popularity ** 3):playlist_subgenre[T.pop edm]                                                       7.2999      3.629      2.012      0.044       0.187      14.413
I(playlist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop]                                                 5.9622      2.823      2.112      0.035       0.429      11.495
I(playlist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house]                                    -0.6997      4.494     -0.156      0.876      -9.509       8.109
I(playlist_avg_popularity ** 3):playlist_subgenre[T.reggaeton]                                                    -3.7654      3.942     -0.955      0.339     -11.492       3.961
I(playlist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop]                                              0.0337      2.293      0.015      0.988      -4.461       4.528
I(playlist_avg_popularity ** 3):playlist_subgenre[T.trap]                                                         12.9336     16.376      0.790      0.430     -19.164      45.032
I(playlist_avg_popularity ** 3):playlist_subgenre[T.tropical]                                                     43.5202     21.246      2.048      0.041       1.878      85.163
I(playlist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary]                                            5.9065      3.974      1.486      0.137      -1.883      13.696
I(danceability ** 3)                                                                                               0.1990      0.385      0.517      0.605      -0.556       0.954
I(danceability ** 3):playlist_subgenre[T.big room]                                                                -0.2372      0.518     -0.458      0.647      -1.253       0.778
I(danceability ** 3):playlist_subgenre[T.classic rock]                                                            -0.0624      0.506     -0.123      0.902      -1.054       0.929
I(danceability ** 3):playlist_subgenre[T.dance pop]                                                               -0.2145      0.524     -0.409      0.682      -1.241       0.812
I(danceability ** 3):playlist_subgenre[T.electro house]                                                           -0.2529      0.653     -0.387      0.698      -1.532       1.026
I(danceability ** 3):playlist_subgenre[T.electropop]                                                              -0.5509      0.451     -1.222      0.222      -1.434       0.332
I(danceability ** 3):playlist_subgenre[T.gangster rap]                                                             0.5042      0.652      0.773      0.439      -0.774       1.783
I(danceability ** 3):playlist_subgenre[T.hard rock]                                                               -0.4396      0.684     -0.643      0.520      -1.780       0.901
I(danceability ** 3):playlist_subgenre[T.hip hop]                                                                 -0.6871      0.554     -1.239      0.215      -1.774       0.399
I(danceability ** 3):playlist_subgenre[T.hip pop]                                                                  0.1799      0.590      0.305      0.760      -0.976       1.336
I(danceability ** 3):playlist_subgenre[T.indie poptimism]                                                          0.1569      0.445      0.353      0.724      -0.715       1.029
I(danceability ** 3):playlist_subgenre[T.latin hip hop]                                                           -1.1399      0.808     -1.412      0.158      -2.723       0.443
I(danceability ** 3):playlist_subgenre[T.latin pop]                                                               -0.1019      0.544     -0.187      0.851      -1.169       0.965
I(danceability ** 3):playlist_subgenre[T.neo soul]                                                                -0.1957      0.455     -0.430      0.667      -1.087       0.696
I(danceability ** 3):playlist_subgenre[T.new jack swing]                                                           0.6583      0.976      0.674      0.500      -1.255       2.571
I(danceability ** 3):playlist_subgenre[T.permanent wave]                                                           0.3969      0.539      0.736      0.462      -0.660       1.454
I(danceability ** 3):playlist_subgenre[T.pop edm]                                                                  0.0712      0.541      0.132      0.895      -0.990       1.132
I(danceability ** 3):playlist_subgenre[T.post-teen pop]                                                           -0.7596      0.504     -1.507      0.132      -1.748       0.229
I(danceability ** 3):playlist_subgenre[T.progressive electro house]                                               -0.6631      0.573     -1.158      0.247      -1.786       0.459
I(danceability ** 3):playlist_subgenre[T.reggaeton]                                                                3.2803      1.583      2.072      0.038       0.177       6.383
I(danceability ** 3):playlist_subgenre[T.southern hip hop]                                                         0.1054      0.438      0.240      0.810      -0.754       0.965
I(danceability ** 3):playlist_subgenre[T.trap]                                                                     0.5929      0.574      1.032      0.302      -0.533       1.719
I(danceability ** 3):playlist_subgenre[T.tropical]                                                                -0.2886      0.490     -0.589      0.556      -1.249       0.672
I(danceability ** 3):playlist_subgenre[T.urban contemporary]                                                      -0.3655      0.440     -0.831      0.406      -1.228       0.497
I(energy ** 3)                                                                                                     0.3228      0.372      0.868      0.385      -0.406       1.052
I(energy ** 3):playlist_subgenre[T.big room]                                                                       0.5245      1.675      0.313      0.754      -2.759       3.808
I(energy ** 3):playlist_subgenre[T.classic rock]                                                                   0.2548      0.521      0.489      0.625      -0.766       1.276
I(energy ** 3):playlist_subgenre[T.dance pop]                                                                     -0.5987      0.520     -1.151      0.250      -1.618       0.420
I(energy ** 3):playlist_subgenre[T.electro house]                                                                 -0.4249      0.514     -0.827      0.408      -1.432       0.582
I(energy ** 3):playlist_subgenre[T.electropop]                                                                    -0.9024      0.508     -1.776      0.076      -1.898       0.094
I(energy ** 3):playlist_subgenre[T.gangster rap]                                                                  -0.3602      0.599     -0.602      0.547      -1.533       0.813
I(energy ** 3):playlist_subgenre[T.hard rock]                                                                     -0.6087      0.559     -1.090      0.276      -1.704       0.486
I(energy ** 3):playlist_subgenre[T.hip hop]                                                                        0.1016      0.644      0.158      0.875      -1.161       1.364
I(energy ** 3):playlist_subgenre[T.hip pop]                                                                       -0.4562      0.800     -0.570      0.569      -2.025       1.113
I(energy ** 3):playlist_subgenre[T.indie poptimism]                                                                0.5312      0.571      0.930      0.353      -0.589       1.651
I(energy ** 3):playlist_subgenre[T.latin hip hop]                                                                 -0.9984      0.569     -1.754      0.079      -2.114       0.117
I(energy ** 3):playlist_subgenre[T.latin pop]                                                                      0.2383      0.567      0.420      0.674      -0.873       1.349
I(energy ** 3):playlist_subgenre[T.neo soul]                                                                       0.3952      0.610      0.647      0.517      -0.801       1.592
I(energy ** 3):playlist_subgenre[T.new jack swing]                                                                -1.0457      0.562     -1.861      0.063      -2.147       0.055
I(energy ** 3):playlist_subgenre[T.permanent wave]                                                                -0.1735      0.530     -0.328      0.743      -1.211       0.864
I(energy ** 3):playlist_subgenre[T.pop edm]                                                                       -0.5803      0.732     -0.793      0.428      -2.014       0.854
I(energy ** 3):playlist_subgenre[T.post-teen pop]                                                                 -0.2599      0.551     -0.472      0.637      -1.340       0.820
I(energy ** 3):playlist_subgenre[T.progressive electro house]                                                     -1.6073      1.202     -1.337      0.181      -3.963       0.749
I(energy ** 3):playlist_subgenre[T.reggaeton]                                                                      4.4321      2.358      1.879      0.060      -0.190       9.055
I(energy ** 3):playlist_subgenre[T.southern hip hop]                                                              -0.3764      0.576     -0.654      0.513      -1.505       0.752
I(energy ** 3):playlist_subgenre[T.trap]                                                                          -0.8413      0.573     -1.467      0.142      -1.965       0.283
I(energy ** 3):playlist_subgenre[T.tropical]                                                                      -0.2376      0.589     -0.404      0.687      -1.391       0.916
I(energy ** 3):playlist_subgenre[T.urban contemporary]                                                             0.0259      0.653      0.040      0.968      -1.255       1.306
I(valence ** 3)                                                                                                   -0.4365      0.780     -0.559      0.576      -1.966       1.093
I(valence ** 3):playlist_subgenre[T.big room]                                                                      1.2427      1.083      1.148      0.251      -0.880       3.365
I(valence ** 3):playlist_subgenre[T.classic rock]                                                                 -0.4502      1.209     -0.373      0.709      -2.819       1.919
I(valence ** 3):playlist_subgenre[T.dance pop]                                                                    -0.7714      1.083     -0.712      0.476      -2.894       1.351
I(valence ** 3):playlist_subgenre[T.electro house]                                                                -0.0741      0.980     -0.076      0.940      -1.995       1.847
I(valence ** 3):playlist_subgenre[T.electropop]                                                                    0.0723      1.051      0.069      0.945      -1.988       2.133
I(valence ** 3):playlist_subgenre[T.gangster rap]                                                                  0.0234      1.023      0.023      0.982      -1.982       2.029
I(valence ** 3):playlist_subgenre[T.hard rock]                                                                     0.9972      1.129      0.883      0.377      -1.216       3.211
I(valence ** 3):playlist_subgenre[T.hip hop]                                                                       1.8362      1.050      1.748      0.080      -0.222       3.895
I(valence ** 3):playlist_subgenre[T.hip pop]                                                                       1.1960      1.204      0.994      0.320      -1.163       3.555
I(valence ** 3):playlist_subgenre[T.indie poptimism]                                                               0.3733      0.998      0.374      0.708      -1.583       2.329
I(valence ** 3):playlist_subgenre[T.latin hip hop]                                                                 1.4700      1.186      1.239      0.215      -0.855       3.795
I(valence ** 3):playlist_subgenre[T.latin pop]                                                                     0.6063      1.207      0.502      0.615      -1.760       2.973
I(valence ** 3):playlist_subgenre[T.neo soul]                                                                     -0.0436      1.056     -0.041      0.967      -2.114       2.026
I(valence ** 3):playlist_subgenre[T.new jack swing]                                                                1.6914      1.399      1.209      0.227      -1.051       4.434
I(valence ** 3):playlist_subgenre[T.permanent wave]                                                                1.0159      1.156      0.879      0.380      -1.250       3.282
I(valence ** 3):playlist_subgenre[T.pop edm]                                                                       0.9962      1.113      0.895      0.371      -1.186       3.178
I(valence ** 3):playlist_subgenre[T.post-teen pop]                                                                 0.0588      1.221      0.048      0.962      -2.335       2.452
I(valence ** 3):playlist_subgenre[T.progressive electro house]                                                     0.2106      0.963      0.219      0.827      -1.677       2.099
I(valence ** 3):playlist_subgenre[T.reggaeton]                                                                    -2.0878      1.896     -1.101      0.271      -5.804       1.629
I(valence ** 3):playlist_subgenre[T.southern hip hop]                                                              0.7320      1.056      0.693      0.488      -1.338       2.802
I(valence ** 3):playlist_subgenre[T.trap]                                                                          0.8263      1.045      0.791      0.429      -1.222       2.875
I(valence ** 3):playlist_subgenre[T.tropical]                                                                     -1.2864      1.049     -1.226      0.220      -3.343       0.771
I(valence ** 3):playlist_subgenre[T.urban contemporary]                                                            1.3076      1.044      1.253      0.210      -0.738       3.353
I(tempo ** 3)                                                                                                      0.0515      0.125      0.411      0.681      -0.194       0.297
I(tempo ** 3):playlist_subgenre[T.big room]                                                                       -0.3281      1.241     -0.264      0.792      -2.761       2.105
I(tempo ** 3):playlist_subgenre[T.classic rock]                                                                   -0.3419      0.315     -1.087      0.277      -0.959       0.275
I(tempo ** 3):playlist_subgenre[T.dance pop]                                                                      -0.0782      0.358     -0.219      0.827      -0.779       0.623
I(tempo ** 3):playlist_subgenre[T.electro house]                                                                  -0.0251      0.783     -0.032      0.974      -1.561       1.510
I(tempo ** 3):playlist_subgenre[T.electropop]                                                                     -0.3229      0.478     -0.675      0.500      -1.260       0.614
I(tempo ** 3):playlist_subgenre[T.gangster rap]                                                                   -0.2686      0.314     -0.855      0.393      -0.884       0.347
I(tempo ** 3):playlist_subgenre[T.hard rock]                                                                      -0.4763      0.490     -0.973      0.331      -1.436       0.483
I(tempo ** 3):playlist_subgenre[T.hip hop]                                                                        -0.0762      0.196     -0.388      0.698      -0.461       0.309
I(tempo ** 3):playlist_subgenre[T.hip pop]                                                                         0.3039      0.333      0.913      0.361      -0.348       0.956
I(tempo ** 3):playlist_subgenre[T.indie poptimism]                                                                -0.5295      0.365     -1.450      0.147      -1.245       0.186
I(tempo ** 3):playlist_subgenre[T.latin hip hop]                                                                   0.1006      0.322      0.313      0.754      -0.530       0.731
I(tempo ** 3):playlist_subgenre[T.latin pop]                                                                      -0.2120      0.442     -0.479      0.632      -1.079       0.655
I(tempo ** 3):playlist_subgenre[T.neo soul]                                                                       -0.0467      0.224     -0.209      0.835      -0.485       0.392
I(tempo ** 3):playlist_subgenre[T.new jack swing]                                                                  0.1271      0.518      0.245      0.806      -0.889       1.143
I(tempo ** 3):playlist_subgenre[T.permanent wave]                                                                 -0.1062      0.278     -0.382      0.702      -0.650       0.438
I(tempo ** 3):playlist_subgenre[T.pop edm]                                                                        -0.0419      0.530     -0.079      0.937      -1.081       0.997
I(tempo ** 3):playlist_subgenre[T.post-teen pop]                                                                   0.0994      0.460      0.216      0.829      -0.802       1.001
I(tempo ** 3):playlist_subgenre[T.progressive electro house]                                                       0.0730      1.332      0.055      0.956      -2.539       2.684
I(tempo ** 3):playlist_subgenre[T.reggaeton]                                                                      -0.7172      0.649     -1.106      0.269      -1.989       0.554
I(tempo ** 3):playlist_subgenre[T.southern hip hop]                                                               -0.1978      0.282     -0.702      0.483      -0.751       0.355
I(tempo ** 3):playlist_subgenre[T.trap]                                                                            0.7734      0.654      1.183      0.237      -0.508       2.055
I(tempo ** 3):playlist_subgenre[T.tropical]                                                                       -0.7687      0.528     -1.455      0.146      -1.804       0.267
I(tempo ** 3):playlist_subgenre[T.urban contemporary]                                                              0.1227      0.358      0.343      0.732      -0.580       0.825
I(duration_ms ** 3)                                                                                                0.1896      0.105      1.811      0.070      -0.016       0.395
I(duration_ms ** 3):playlist_subgenre[T.big room]                                                                 -0.1102      0.711     -0.155      0.877      -1.503       1.283
I(duration_ms ** 3):playlist_subgenre[T.classic rock]                                                             -0.4854      0.322     -1.509      0.131      -1.116       0.145
I(duration_ms ** 3):playlist_subgenre[T.dance pop]                                                                -0.1882      0.504     -0.373      0.709      -1.177       0.801
I(duration_ms ** 3):playlist_subgenre[T.electro house]                                                            -0.1405      0.120     -1.168      0.243      -0.376       0.095
I(duration_ms ** 3):playlist_subgenre[T.electropop]                                                                0.3583      0.292      1.226      0.220      -0.215       0.931
I(duration_ms ** 3):playlist_subgenre[T.gangster rap]                                                             -0.3174      0.213     -1.490      0.136      -0.735       0.100
I(duration_ms ** 3):playlist_subgenre[T.hard rock]                                                                -0.1468      0.309     -0.475      0.635      -0.753       0.459
I(duration_ms ** 3):playlist_subgenre[T.hip hop]                                                                  -0.1190      0.174     -0.685      0.493      -0.460       0.222
I(duration_ms ** 3):playlist_subgenre[T.hip pop]                                                                  -0.2361      0.220     -1.073      0.283      -0.667       0.195
I(duration_ms ** 3):playlist_subgenre[T.indie poptimism]                                                          -0.3843      0.492     -0.781      0.435      -1.349       0.580
I(duration_ms ** 3):playlist_subgenre[T.latin hip hop]                                                            -0.2322      0.207     -1.123      0.262      -0.637       0.173
I(duration_ms ** 3):playlist_subgenre[T.latin pop]                                                                -0.2180      0.365     -0.597      0.550      -0.934       0.498
I(duration_ms ** 3):playlist_subgenre[T.neo soul]                                                                 -0.4898      0.221     -2.213      0.027      -0.924      -0.056
I(duration_ms ** 3):playlist_subgenre[T.new jack swing]                                                           -0.4285      0.188     -2.278      0.023      -0.797      -0.060
I(duration_ms ** 3):playlist_subgenre[T.permanent wave]                                                            0.2006      0.428      0.469      0.639      -0.638       1.039
I(duration_ms ** 3):playlist_subgenre[T.pop edm]                                                                  -0.6275      0.561     -1.119      0.263      -1.727       0.472
I(duration_ms ** 3):playlist_subgenre[T.post-teen pop]                                                            -0.6304      0.268     -2.356      0.018      -1.155      -0.106
I(duration_ms ** 3):playlist_subgenre[T.progressive electro house]                                                 0.0054      0.283      0.019      0.985      -0.549       0.560
I(duration_ms ** 3):playlist_subgenre[T.reggaeton]                                                                 0.3751      0.583      0.643      0.520      -0.767       1.518
I(duration_ms ** 3):playlist_subgenre[T.southern hip hop]                                                         -0.2811      0.122     -2.295      0.022      -0.521      -0.041
I(duration_ms ** 3):playlist_subgenre[T.trap]                                                                      0.1298      0.412      0.315      0.753      -0.678       0.937
I(duration_ms ** 3):playlist_subgenre[T.tropical]                                                                 -0.2456      0.188     -1.308      0.191      -0.614       0.123
I(duration_ms ** 3):playlist_subgenre[T.urban contemporary]                                                       -0.5350      0.218     -2.459      0.014      -0.961      -0.109
I(artist_hit_rate ** 3)                                                                                            3.2005      2.885      1.109      0.267      -2.454       8.855
I(artist_hit_rate ** 3):playlist_subgenre[T.big room]                                                             -4.7891      8.628     -0.555      0.579     -21.700      12.121
I(artist_hit_rate ** 3):playlist_subgenre[T.classic rock]                                                        -10.0471      4.020     -2.499      0.012     -17.927      -2.168
I(artist_hit_rate ** 3):playlist_subgenre[T.dance pop]                                                             2.2625      3.708      0.610      0.542      -5.005       9.530
I(artist_hit_rate ** 3):playlist_subgenre[T.electro house]                                                        14.4122      7.847      1.837      0.066      -0.969      29.793
I(artist_hit_rate ** 3):playlist_subgenre[T.electropop]                                                           -0.3761      3.598     -0.105      0.917      -7.429       6.677
I(artist_hit_rate ** 3):playlist_subgenre[T.gangster rap]                                                         -3.7236      3.678     -1.012      0.311     -10.933       3.486
I(artist_hit_rate ** 3):playlist_subgenre[T.hard rock]                                                            -0.7139      4.116     -0.173      0.862      -8.781       7.353
I(artist_hit_rate ** 3):playlist_subgenre[T.hip hop]                                                              -6.2794      3.910     -1.606      0.108     -13.943       1.384
I(artist_hit_rate ** 3):playlist_subgenre[T.hip pop]                                                              -5.1457      4.507     -1.142      0.254     -13.979       3.688
I(artist_hit_rate ** 3):playlist_subgenre[T.indie poptimism]                                                     -10.3522      4.116     -2.515      0.012     -18.419      -2.285
I(artist_hit_rate ** 3):playlist_subgenre[T.latin hip hop]                                                        -3.7359      4.000     -0.934      0.350     -11.577       4.105
I(artist_hit_rate ** 3):playlist_subgenre[T.latin pop]                                                            -2.9068      3.804     -0.764      0.445     -10.362       4.548
I(artist_hit_rate ** 3):playlist_subgenre[T.neo soul]                                                             -6.0084      4.542     -1.323      0.186     -14.912       2.895
I(artist_hit_rate ** 3):playlist_subgenre[T.new jack swing]                                                       -6.4789     17.730     -0.365      0.715     -41.230      28.272
I(artist_hit_rate ** 3):playlist_subgenre[T.permanent wave]                                                        2.5716      3.938      0.653      0.514      -5.147      10.290
I(artist_hit_rate ** 3):playlist_subgenre[T.pop edm]                                                              -1.0555      4.403     -0.240      0.811      -9.686       7.575
I(artist_hit_rate ** 3):playlist_subgenre[T.post-teen pop]                                                        -2.4475      3.617     -0.677      0.499      -9.538       4.643
I(artist_hit_rate ** 3):playlist_subgenre[T.progressive electro house]                                            -5.9912      7.550     -0.794      0.427     -20.789       8.806
I(artist_hit_rate ** 3):playlist_subgenre[T.reggaeton]                                                            -2.8819      3.729     -0.773      0.440     -10.191       4.428
I(artist_hit_rate ** 3):playlist_subgenre[T.southern hip hop]                                                      7.5348      4.543      1.659      0.097      -1.369      16.439
I(artist_hit_rate ** 3):playlist_subgenre[T.trap]                                                                 -5.0470      3.710     -1.360      0.174     -12.318       2.224
I(artist_hit_rate ** 3):playlist_subgenre[T.tropical]                                                            -11.3145      4.720     -2.397      0.017     -20.565      -2.064
I(artist_hit_rate ** 3):playlist_subgenre[T.urban contemporary]                                                   -1.2146      3.830     -0.317      0.751      -8.721       6.292
I(artist_n_tracks ** 3)                                                                                           -1.2427      0.584     -2.128      0.033      -2.387      -0.098
I(artist_n_tracks ** 3):playlist_subgenre[T.big room]                                                             -0.2866      0.918     -0.312      0.755      -2.085       1.512
I(artist_n_tracks ** 3):playlist_subgenre[T.classic rock]                                                         -0.7137      0.827     -0.863      0.388      -2.334       0.907
I(artist_n_tracks ** 3):playlist_subgenre[T.dance pop]                                                             0.7758      0.817      0.950      0.342      -0.825       2.376
I(artist_n_tracks ** 3):playlist_subgenre[T.electro house]                                                         1.0229      0.881      1.162      0.245      -0.703       2.749
I(artist_n_tracks ** 3):playlist_subgenre[T.electropop]                                                            1.6680      0.802      2.079      0.038       0.096       3.240
I(artist_n_tracks ** 3):playlist_subgenre[T.gangster rap]                                                          1.1926      1.049      1.137      0.256      -0.864       3.249
I(artist_n_tracks ** 3):playlist_subgenre[T.hard rock]                                                             1.0827      0.825      1.313      0.189      -0.533       2.699
I(artist_n_tracks ** 3):playlist_subgenre[T.hip hop]                                                               1.7451      1.230      1.419      0.156      -0.666       4.156
I(artist_n_tracks ** 3):playlist_subgenre[T.hip pop]                                                              -1.3331      1.555     -0.857      0.391      -4.380       1.714
I(artist_n_tracks ** 3):playlist_subgenre[T.indie poptimism]                                                       3.7295      1.187      3.141      0.002       1.402       6.057
I(artist_n_tracks ** 3):playlist_subgenre[T.latin hip hop]                                                         3.2381      0.897      3.610      0.000       1.480       4.996
I(artist_n_tracks ** 3):playlist_subgenre[T.latin pop]                                                             0.5250      0.976      0.538      0.590      -1.387       2.437
I(artist_n_tracks ** 3):playlist_subgenre[T.neo soul]                                                              1.7630      1.597      1.104      0.270      -1.367       4.893
I(artist_n_tracks ** 3):playlist_subgenre[T.new jack swing]                                                        0.2024      1.433      0.141      0.888      -2.607       3.012
I(artist_n_tracks ** 3):playlist_subgenre[T.permanent wave]                                                        1.3165      0.948      1.389      0.165      -0.541       3.174
I(artist_n_tracks ** 3):playlist_subgenre[T.pop edm]                                                               1.0125      0.935      1.084      0.279      -0.819       2.844
I(artist_n_tracks ** 3):playlist_subgenre[T.post-teen pop]                                                         1.2006      0.842      1.426      0.154      -0.450       2.851
I(artist_n_tracks ** 3):playlist_subgenre[T.progressive electro house]                                             1.8730      0.827      2.265      0.024       0.252       3.494
I(artist_n_tracks ** 3):playlist_subgenre[T.reggaeton]                                                             1.3049      0.991      1.316      0.188      -0.638       3.248
I(artist_n_tracks ** 3):playlist_subgenre[T.southern hip hop]                                                      1.4305      0.841      1.701      0.089      -0.217       3.078
I(artist_n_tracks ** 3):playlist_subgenre[T.trap]                                                                  0.6050      1.173      0.516      0.606      -1.694       2.904
I(artist_n_tracks ** 3):playlist_subgenre[T.tropical]                                                              0.6685      1.385      0.483      0.629      -2.046       3.383
I(artist_n_tracks ** 3):playlist_subgenre[T.urban contemporary]                                                    1.5519      1.042      1.489      0.136      -0.491       3.595
artist_avg_popularity:I(artist_avg_popularity ** 2)                                                                3.9201      1.511      2.594      0.010       0.958       6.883
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.big room]                                 -1.9467      2.473     -0.787      0.431      -6.795       2.901
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.classic rock]                              0.4206      2.127      0.198      0.843      -3.749       4.590
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.dance pop]                                -1.9528      1.934     -1.010      0.313      -5.743       1.837
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.electro house]                            -2.5991      2.200     -1.182      0.237      -6.911       1.713
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.electropop]                               -0.1635      1.932     -0.085      0.933      -3.951       3.623
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.gangster rap]                             -0.9812      2.070     -0.474      0.635      -5.038       3.075
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.hard rock]                                -0.2852      2.035     -0.140      0.889      -4.273       3.703
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.hip hop]                                  -0.2657      2.000     -0.133      0.894      -4.186       3.655
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.hip pop]                                  -3.0710      2.021     -1.520      0.129      -7.032       0.890
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism]                          -2.3894      1.828     -1.307      0.191      -5.972       1.193
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop]                            -3.0958      1.938     -1.598      0.110      -6.894       0.702
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.latin pop]                                -4.6036      1.999     -2.303      0.021      -8.522      -0.685
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.neo soul]                                 -1.9739      1.860     -1.061      0.289      -5.619       1.671
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.new jack swing]                           -0.8604      2.728     -0.315      0.752      -6.207       4.486
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.permanent wave]                           -6.5769      2.000     -3.289      0.001     -10.497      -2.657
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.pop edm]                                  -0.1156      2.228     -0.052      0.959      -4.483       4.251
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop]                            -5.0715      1.899     -2.671      0.008      -8.793      -1.350
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house]                -0.2674      2.127     -0.126      0.900      -4.436       3.901
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.reggaeton]                                -1.2440      3.146     -0.395      0.693      -7.411       4.923
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop]                         -2.1137      1.927     -1.097      0.273      -5.890       1.662
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.trap]                                     -0.6778      2.138     -0.317      0.751      -4.869       3.513
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.tropical]                                 -2.3042      2.067     -1.115      0.265      -6.356       1.747
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary]                       -0.4825      1.944     -0.248      0.804      -4.294       3.328
artist_avg_popularity:I(artist_avg_popularity ** 3)                                                                3.8379      1.579      2.431      0.015       0.743       6.933
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.big room]                                 -3.2219      2.326     -1.385      0.166      -7.780       1.336
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.classic rock]                             -0.3047      2.127     -0.143      0.886      -4.474       3.865
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.dance pop]                                -2.0866      2.192     -0.952      0.341      -6.383       2.210
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.electro house]                            -4.5854      2.205     -2.079      0.038      -8.908      -0.263
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.electropop]                               -1.5439      1.993     -0.775      0.439      -5.451       2.363
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.gangster rap]                             -2.4016      2.058     -1.167      0.243      -6.435       1.632
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.hard rock]                                -1.4115      2.130     -0.663      0.508      -5.587       2.764
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.hip hop]                                  -0.8678      2.912     -0.298      0.766      -6.576       4.841
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.hip pop]                                  -3.3700      2.167     -1.555      0.120      -7.618       0.878
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism]                          -3.2625      1.882     -1.734      0.083      -6.951       0.426
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop]                            -3.8021      1.999     -1.902      0.057      -7.720       0.116
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.latin pop]                                -4.9887      2.291     -2.178      0.029      -9.479      -0.499
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.neo soul]                                 -2.6462      1.841     -1.437      0.151      -6.255       0.963
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.new jack swing]                           -2.7996      2.532     -1.106      0.269      -7.762       2.163
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.permanent wave]                           -6.5834      2.238     -2.941      0.003     -10.971      -2.196
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.pop edm]                                  -0.7018      2.336     -0.300      0.764      -5.281       3.877
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop]                            -5.2663      2.121     -2.483      0.013      -9.424      -1.108
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house]                -1.9180      1.995     -0.961      0.336      -5.828       1.992
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.reggaeton]                                -2.5725      4.172     -0.617      0.537     -10.749       5.604
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop]                         -2.9554      1.974     -1.497      0.134      -6.824       0.913
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.trap]                                     -1.0255      2.561     -0.400      0.689      -6.046       3.995
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.tropical]                                 -3.2578      2.234     -1.458      0.145      -7.637       1.121
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary]                       -1.5730      2.086     -0.754      0.451      -5.661       2.515
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3)                                                        0.5164      0.222      2.330      0.020       0.082       0.951
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.big room]                         -0.4908      0.312     -1.575      0.115      -1.102       0.120
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.classic rock]                     -0.0847      0.290     -0.292      0.770      -0.653       0.484
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.dance pop]                        -0.2951      0.320     -0.922      0.356      -0.922       0.332
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.electro house]                    -0.7152      0.303     -2.362      0.018      -1.309      -0.122
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.electropop]                       -0.2825      0.278     -1.018      0.309      -0.827       0.262
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.gangster rap]                     -0.3767      0.284     -1.325      0.185      -0.934       0.181
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.hard rock]                        -0.2323      0.299     -0.777      0.437      -0.818       0.353
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.hip hop]                          -0.1965      0.551     -0.357      0.721      -1.276       0.883
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.hip pop]                          -0.4590      0.306     -1.502      0.133      -1.058       0.140
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism]                  -0.4689      0.262     -1.793      0.073      -0.981       0.044
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop]                    -0.5330      0.280     -1.901      0.057      -1.083       0.017
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.latin pop]                        -0.6591      0.341     -1.931      0.054      -1.328       0.010
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.neo soul]                         -0.3831      0.253     -1.516      0.130      -0.879       0.112
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.new jack swing]                   -0.4571      0.339     -1.347      0.178      -1.122       0.208
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.permanent wave]                   -0.8780      0.327     -2.684      0.007      -1.519      -0.237
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.pop edm]                          -0.1210      0.325     -0.372      0.710      -0.758       0.516
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop]                    -0.7083      0.309     -2.292      0.022      -1.314      -0.103
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house]        -0.3369      0.269     -1.254      0.210      -0.864       0.190
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.reggaeton]                        -0.4128      0.603     -0.685      0.494      -1.595       0.769
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop]                 -0.4300      0.275     -1.563      0.118      -0.969       0.109
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.trap]                             -0.1769      0.382     -0.462      0.644      -0.927       0.573
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.tropical]                         -0.4792      0.321     -1.491      0.136      -1.109       0.151
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary]               -0.2829      0.296     -0.954      0.340      -0.864       0.298
playlist_avg_popularity:I(playlist_avg_popularity ** 2)                                                            0.8439      0.646      1.307      0.191      -0.422       2.110
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.big room]                             20.3354      9.298      2.187      0.029       2.112      38.559
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.classic rock]                         -8.1745      3.566     -2.293      0.022     -15.164      -1.185
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.dance pop]                           -46.1502     42.763     -1.079      0.280    -129.967      37.667
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.electro house]                         1.5047      1.702      0.884      0.377      -1.832       4.841
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.electropop]                            0.1956      0.800      0.245      0.807      -1.372       1.763
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.gangster rap]                          5.0763      2.035      2.494      0.013       1.087       9.066
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.hard rock]                            -1.0363      1.983     -0.522      0.601      -4.924       2.851
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip hop]                            -523.2436    260.620     -2.008      0.045   -1034.072     -12.416
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip pop]                              -8.3433      7.455     -1.119      0.263     -22.956       6.269
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism]                      -0.1076      4.171     -0.026      0.979      -8.282       8.067
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop]                        -0.3871      0.869     -0.446      0.656      -2.090       1.315
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin pop]                             1.1257      2.185      0.515      0.606      -3.156       5.408
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.neo soul]                              0.1801      1.359      0.132      0.895      -2.484       2.844
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.new jack swing]                        3.2099      8.194      0.392      0.695     -12.851      19.271
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave]                      139.1233     40.043      3.474      0.001      60.637     217.610
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.pop edm]                               7.2999      3.629      2.012      0.044       0.187      14.413
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop]                         5.9622      2.823      2.112      0.035       0.429      11.495
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house]            -0.6997      4.494     -0.156      0.876      -9.509       8.109
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.reggaeton]                            -3.7654      3.942     -0.955      0.339     -11.492       3.961
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop]                      0.0337      2.293      0.015      0.988      -4.461       4.528
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.trap]                                 12.9336     16.376      0.790      0.430     -19.164      45.032
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.tropical]                             43.5202     21.246      2.048      0.041       1.878      85.163
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary]                    5.9065      3.974      1.486      0.137      -1.883      13.696
playlist_avg_popularity:I(playlist_avg_popularity ** 3)                                                            0.9685      1.925      0.503      0.615      -2.805       4.742
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.big room]                             28.9964     12.559      2.309      0.021       4.380      53.613
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.classic rock]                          5.3943      3.703      1.457      0.145      -1.864      12.652
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.dance pop]                            82.5944     69.888      1.182      0.237     -54.389     219.578
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.electro house]                         3.6027      4.164      0.865      0.387      -4.559      11.765
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.electropop]                            0.3086      2.397      0.129      0.898      -4.389       5.006
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.gangster rap]                        -10.8337      3.265     -3.318      0.001     -17.234      -4.433
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.hard rock]                            -3.5263      4.740     -0.744      0.457     -12.818       5.765
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip hop]                             586.8161    289.253      2.029      0.042      19.865    1153.767
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip pop]                             -14.2595      7.257     -1.965      0.049     -28.484      -0.035
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism]                       2.4707      2.838      0.871      0.384      -3.092       8.034
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop]                        -1.0344      2.327     -0.444      0.657      -5.596       3.527
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin pop]                           -11.6439      8.915     -1.306      0.192     -29.117       5.829
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.neo soul]                              3.8562      3.356      1.149      0.251      -2.722      10.434
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.new jack swing]                       -5.2009     15.943     -0.326      0.744     -36.449      26.047
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.permanent wave]                     -247.8851     86.565     -2.864      0.004    -417.558     -78.212
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.pop edm]                              -8.1664      2.626     -3.110      0.002     -13.314      -3.019
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop]                        46.9376     16.078      2.919      0.004      15.425      78.451
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house]            -2.4659      4.604     -0.536      0.592     -11.490       6.559
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.reggaeton]                            -3.2323      4.867     -0.664      0.507     -12.771       6.306
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop]                    -14.8098      8.171     -1.812      0.070     -30.826       1.206
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.trap]                                 -7.3908     51.361     -0.144      0.886    -108.061      93.280
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.tropical]                             16.3813     19.498      0.840      0.401     -21.836      54.598
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary]                   -2.0841      2.863     -0.728      0.467      -7.695       3.527
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3)                                                    0.1623      0.393      0.413      0.679      -0.608       0.932
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.big room]                      5.7496      2.456      2.341      0.019       0.935      10.564
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.classic rock]                 10.5957      4.156      2.550      0.011       2.450      18.741
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.dance pop]                   -23.6436     18.887     -1.252      0.211     -60.664      13.376
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.electro house]                 1.0371      1.045      0.992      0.321      -1.012       3.086
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.electropop]                    0.1411      0.551      0.256      0.798      -0.939       1.221
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.gangster rap]                 -7.2674      1.968     -3.693      0.000     -11.125      -3.410
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.hard rock]                    -0.8214      1.070     -0.767      0.443      -2.920       1.277
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip hop]                    -122.1359     59.733     -2.045      0.041    -239.216      -5.056
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip pop]                      10.9449      7.831      1.398      0.162      -4.403      26.293
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism]              -0.9648      4.461     -0.216      0.829      -9.708       7.779
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop]                -0.1786      0.457     -0.391      0.696      -1.075       0.718
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin pop]                     3.4410      4.140      0.831      0.406      -4.674      11.556
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.neo soul]                      0.8469      0.663      1.276      0.202      -0.454       2.147
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.new jack swing]               -4.0294      4.610     -0.874      0.382     -13.065       5.006
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.permanent wave]               71.4682     28.834      2.479      0.013      14.953     127.983
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.pop edm]                      -8.9968      2.968     -3.031      0.002     -14.814      -3.180
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop]               -20.8071      6.830     -3.046      0.002     -34.195      -7.420
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house]    -0.5112      0.742     -0.689      0.491      -1.966       0.943
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.reggaeton]                     2.1228      3.706      0.573      0.567      -5.141       9.386
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop]             -7.1547      4.207     -1.701      0.089     -15.400       1.091
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.trap]                         -4.3697     21.119     -0.207      0.836     -45.764      37.025
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.tropical]                    -94.2655     50.626     -1.862      0.063    -193.495       4.964
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary]           -4.9454      3.241     -1.526      0.127     -11.297       1.406
danceability:I(danceability ** 2)                                                                                  0.1990      0.385      0.517      0.605      -0.556       0.954
danceability:I(danceability ** 2):playlist_subgenre[T.big room]                                                   -0.2372      0.518     -0.458      0.647      -1.253       0.778
danceability:I(danceability ** 2):playlist_subgenre[T.classic rock]                                               -0.0624      0.506     -0.123      0.902      -1.054       0.929
danceability:I(danceability ** 2):playlist_subgenre[T.dance pop]                                                  -0.2145      0.524     -0.409      0.682      -1.241       0.812
danceability:I(danceability ** 2):playlist_subgenre[T.electro house]                                              -0.2529      0.653     -0.387      0.698      -1.532       1.026
danceability:I(danceability ** 2):playlist_subgenre[T.electropop]                                                 -0.5509      0.451     -1.222      0.222      -1.434       0.332
danceability:I(danceability ** 2):playlist_subgenre[T.gangster rap]                                                0.5042      0.652      0.773      0.439      -0.774       1.783
danceability:I(danceability ** 2):playlist_subgenre[T.hard rock]                                                  -0.4396      0.684     -0.643      0.520      -1.780       0.901
danceability:I(danceability ** 2):playlist_subgenre[T.hip hop]                                                    -0.6871      0.554     -1.239      0.215      -1.774       0.399
danceability:I(danceability ** 2):playlist_subgenre[T.hip pop]                                                     0.1799      0.590      0.305      0.760      -0.976       1.336
danceability:I(danceability ** 2):playlist_subgenre[T.indie poptimism]                                             0.1569      0.445      0.353      0.724      -0.715       1.029
danceability:I(danceability ** 2):playlist_subgenre[T.latin hip hop]                                              -1.1399      0.808     -1.412      0.158      -2.723       0.443
danceability:I(danceability ** 2):playlist_subgenre[T.latin pop]                                                  -0.1019      0.544     -0.187      0.851      -1.169       0.965
danceability:I(danceability ** 2):playlist_subgenre[T.neo soul]                                                   -0.1957      0.455     -0.430      0.667      -1.087       0.696
danceability:I(danceability ** 2):playlist_subgenre[T.new jack swing]                                              0.6583      0.976      0.674      0.500      -1.255       2.571
danceability:I(danceability ** 2):playlist_subgenre[T.permanent wave]                                              0.3969      0.539      0.736      0.462      -0.660       1.454
danceability:I(danceability ** 2):playlist_subgenre[T.pop edm]                                                     0.0712      0.541      0.132      0.895      -0.990       1.132
danceability:I(danceability ** 2):playlist_subgenre[T.post-teen pop]                                              -0.7596      0.504     -1.507      0.132      -1.748       0.229
danceability:I(danceability ** 2):playlist_subgenre[T.progressive electro house]                                  -0.6631      0.573     -1.158      0.247      -1.786       0.459
danceability:I(danceability ** 2):playlist_subgenre[T.reggaeton]                                                   3.2803      1.583      2.072      0.038       0.177       6.383
danceability:I(danceability ** 2):playlist_subgenre[T.southern hip hop]                                            0.1054      0.438      0.240      0.810      -0.754       0.965
danceability:I(danceability ** 2):playlist_subgenre[T.trap]                                                        0.5929      0.574      1.032      0.302      -0.533       1.719
danceability:I(danceability ** 2):playlist_subgenre[T.tropical]                                                   -0.2886      0.490     -0.589      0.556      -1.249       0.672
danceability:I(danceability ** 2):playlist_subgenre[T.urban contemporary]                                         -0.3655      0.440     -0.831      0.406      -1.228       0.497
danceability:I(danceability ** 3)                                                                                  0.2799      0.541      0.517      0.605      -0.781       1.341
danceability:I(danceability ** 3):playlist_subgenre[T.big room]                                                   -0.6923      0.818     -0.847      0.397      -2.295       0.910
danceability:I(danceability ** 3):playlist_subgenre[T.classic rock]                                               -0.9564      0.737     -1.297      0.195      -2.402       0.489
danceability:I(danceability ** 3):playlist_subgenre[T.dance pop]                                                   0.3606      0.752      0.479      0.632      -1.114       1.835
danceability:I(danceability ** 3):playlist_subgenre[T.electro house]                                              -0.3183      0.647     -0.492      0.623      -1.586       0.949
danceability:I(danceability ** 3):playlist_subgenre[T.electropop]                                                 -0.6581      0.655     -1.004      0.315      -1.942       0.626
danceability:I(danceability ** 3):playlist_subgenre[T.gangster rap]                                               -0.3219      0.678     -0.475      0.635      -1.650       1.006
danceability:I(danceability ** 3):playlist_subgenre[T.hard rock]                                                  -0.5167      0.814     -0.635      0.526      -2.112       1.079
danceability:I(danceability ** 3):playlist_subgenre[T.hip hop]                                                    -0.0091      0.658     -0.014      0.989      -1.299       1.281
danceability:I(danceability ** 3):playlist_subgenre[T.hip pop]                                                    -1.0148      0.785     -1.293      0.196      -2.553       0.523
danceability:I(danceability ** 3):playlist_subgenre[T.indie poptimism]                                             0.0284      0.651      0.044      0.965      -1.247       1.304
danceability:I(danceability ** 3):playlist_subgenre[T.latin hip hop]                                               0.1980      0.697      0.284      0.776      -1.169       1.565
danceability:I(danceability ** 3):playlist_subgenre[T.latin pop]                                                  -0.6707      0.747     -0.897      0.370      -2.136       0.794
danceability:I(danceability ** 3):playlist_subgenre[T.neo soul]                                                   -0.3944      0.670     -0.588      0.556      -1.709       0.920
danceability:I(danceability ** 3):playlist_subgenre[T.new jack swing]                                              0.0957      0.786      0.122      0.903      -1.445       1.636
danceability:I(danceability ** 3):playlist_subgenre[T.permanent wave]                                             -0.1407      0.765     -0.184      0.854      -1.639       1.358
danceability:I(danceability ** 3):playlist_subgenre[T.pop edm]                                                     0.3297      0.813      0.405      0.685      -1.265       1.924
danceability:I(danceability ** 3):playlist_subgenre[T.post-teen pop]                                              -0.0227      0.748     -0.030      0.976      -1.490       1.444
danceability:I(danceability ** 3):playlist_subgenre[T.progressive electro house]                                   0.1922      0.685      0.281      0.779      -1.151       1.535
danceability:I(danceability ** 3):playlist_subgenre[T.reggaeton]                                                   0.8490      1.064      0.798      0.425      -1.236       2.934
danceability:I(danceability ** 3):playlist_subgenre[T.southern hip hop]                                           -0.4102      0.608     -0.675      0.500      -1.602       0.782
danceability:I(danceability ** 3):playlist_subgenre[T.trap]                                                       -1.1495      0.668     -1.722      0.085      -2.458       0.159
danceability:I(danceability ** 3):playlist_subgenre[T.tropical]                                                   -0.1323      0.695     -0.191      0.849      -1.494       1.229
danceability:I(danceability ** 3):playlist_subgenre[T.urban contemporary]                                          0.0021      0.649      0.003      0.997      -1.270       1.274
I(danceability ** 2):I(danceability ** 3)                                                                          0.0557      0.096      0.580      0.562      -0.133       0.244
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.big room]                                           -0.1333      0.164     -0.815      0.415      -0.454       0.187
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.classic rock]                                       -0.2112      0.136     -1.548      0.122      -0.479       0.056
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.dance pop]                                           0.1244      0.181      0.688      0.491      -0.230       0.479
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.electro house]                                      -0.0387      0.217     -0.179      0.858      -0.464       0.386
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.electropop]                                         -0.1027      0.117     -0.874      0.382      -0.333       0.128
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.gangster rap]                                       -0.2272      0.218     -1.042      0.298      -0.655       0.200
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.hard rock]                                          -0.0958      0.134     -0.716      0.474      -0.358       0.166
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.hip hop]                                             0.1198      0.171      0.698      0.485      -0.216       0.456
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.hip pop]                                            -0.3297      0.212     -1.556      0.120      -0.745       0.086
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.indie poptimism]                                    -0.0410      0.122     -0.337      0.736      -0.280       0.198
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.latin hip hop]                                       0.2462      0.292      0.843      0.399      -0.326       0.818
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.latin pop]                                          -0.1553      0.189     -0.821      0.412      -0.526       0.216
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.neo soul]                                           -0.0870      0.135     -0.645      0.519      -0.351       0.177
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.new jack swing]                                     -0.3498      0.392     -0.893      0.372      -1.117       0.418
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.permanent wave]                                     -0.0811      0.141     -0.575      0.565      -0.358       0.195
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.pop edm]                                             0.0702      0.198      0.355      0.722      -0.317       0.458
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.post-teen pop]                                       0.1227      0.175      0.701      0.483      -0.220       0.466
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.progressive electro house]                           0.1717      0.197      0.870      0.384      -0.215       0.559
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.reggaeton]                                          -1.8213      0.737     -2.471      0.013      -3.266      -0.376
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.southern hip hop]                                   -0.1206      0.121     -1.000      0.317      -0.357       0.116
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.trap]                                               -0.3846      0.184     -2.089      0.037      -0.745      -0.024
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.tropical]                                           -0.0286      0.123     -0.234      0.815      -0.269       0.212
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.urban contemporary]                                  0.0347      0.123      0.283      0.777      -0.206       0.275
energy:I(energy ** 2)                                                                                              0.3228      0.372      0.868      0.385      -0.406       1.052
energy:I(energy ** 2):playlist_subgenre[T.big room]                                                                0.5245      1.675      0.313      0.754      -2.759       3.808
energy:I(energy ** 2):playlist_subgenre[T.classic rock]                                                            0.2548      0.521      0.489      0.625      -0.766       1.276
energy:I(energy ** 2):playlist_subgenre[T.dance pop]                                                              -0.5987      0.520     -1.151      0.250      -1.618       0.420
energy:I(energy ** 2):playlist_subgenre[T.electro house]                                                          -0.4249      0.514     -0.827      0.408      -1.432       0.582
energy:I(energy ** 2):playlist_subgenre[T.electropop]                                                             -0.9024      0.508     -1.776      0.076      -1.898       0.094
energy:I(energy ** 2):playlist_subgenre[T.gangster rap]                                                           -0.3602      0.599     -0.602      0.547      -1.533       0.813
energy:I(energy ** 2):playlist_subgenre[T.hard rock]                                                              -0.6087      0.559     -1.090      0.276      -1.704       0.486
energy:I(energy ** 2):playlist_subgenre[T.hip hop]                                                                 0.1016      0.644      0.158      0.875      -1.161       1.364
energy:I(energy ** 2):playlist_subgenre[T.hip pop]                                                                -0.4562      0.800     -0.570      0.569      -2.025       1.113
energy:I(energy ** 2):playlist_subgenre[T.indie poptimism]                                                         0.5312      0.571      0.930      0.353      -0.589       1.651
energy:I(energy ** 2):playlist_subgenre[T.latin hip hop]                                                          -0.9984      0.569     -1.754      0.079      -2.114       0.117
energy:I(energy ** 2):playlist_subgenre[T.latin pop]                                                               0.2383      0.567      0.420      0.674      -0.873       1.349
energy:I(energy ** 2):playlist_subgenre[T.neo soul]                                                                0.3952      0.610      0.647      0.517      -0.801       1.592
energy:I(energy ** 2):playlist_subgenre[T.new jack swing]                                                         -1.0457      0.562     -1.861      0.063      -2.147       0.055
energy:I(energy ** 2):playlist_subgenre[T.permanent wave]                                                         -0.1735      0.530     -0.328      0.743      -1.211       0.864
energy:I(energy ** 2):playlist_subgenre[T.pop edm]                                                                -0.5803      0.732     -0.793      0.428      -2.014       0.854
energy:I(energy ** 2):playlist_subgenre[T.post-teen pop]                                                          -0.2599      0.551     -0.472      0.637      -1.340       0.820
energy:I(energy ** 2):playlist_subgenre[T.progressive electro house]                                              -1.6073      1.202     -1.337      0.181      -3.963       0.749
energy:I(energy ** 2):playlist_subgenre[T.reggaeton]                                                               4.4321      2.358      1.879      0.060      -0.190       9.055
energy:I(energy ** 2):playlist_subgenre[T.southern hip hop]                                                       -0.3764      0.576     -0.654      0.513      -1.505       0.752
energy:I(energy ** 2):playlist_subgenre[T.trap]                                                                   -0.8413      0.573     -1.467      0.142      -1.965       0.283
energy:I(energy ** 2):playlist_subgenre[T.tropical]                                                               -0.2376      0.589     -0.404      0.687      -1.391       0.916
energy:I(energy ** 2):playlist_subgenre[T.urban contemporary]                                                      0.0259      0.653      0.040      0.968      -1.255       1.306
energy:I(energy ** 3)                                                                                              0.0166      0.538      0.031      0.975      -1.039       1.072
energy:I(energy ** 3):playlist_subgenre[T.big room]                                                               -0.6977      1.241     -0.562      0.574      -3.130       1.735
energy:I(energy ** 3):playlist_subgenre[T.classic rock]                                                           -1.1211      0.941     -1.192      0.233      -2.965       0.723
energy:I(energy ** 3):playlist_subgenre[T.dance pop]                                                               0.9447      0.897      1.054      0.292      -0.813       2.702
energy:I(energy ** 3):playlist_subgenre[T.electro house]                                                          -0.1216      0.872     -0.139      0.889      -1.831       1.588
energy:I(energy ** 3):playlist_subgenre[T.electropop]                                                             -1.3110      0.830     -1.580      0.114      -2.937       0.315
energy:I(energy ** 3):playlist_subgenre[T.gangster rap]                                                            1.6094      1.156      1.392      0.164      -0.657       3.876
energy:I(energy ** 3):playlist_subgenre[T.hard rock]                                                               0.6962      0.929      0.750      0.453      -1.124       2.516
energy:I(energy ** 3):playlist_subgenre[T.hip hop]                                                                 0.5663      0.758      0.747      0.455      -0.920       2.052
energy:I(energy ** 3):playlist_subgenre[T.hip pop]                                                                -0.2687      1.105     -0.243      0.808      -2.435       1.897
energy:I(energy ** 3):playlist_subgenre[T.indie poptimism]                                                         0.8189      0.765      1.070      0.285      -0.681       2.319
energy:I(energy ** 3):playlist_subgenre[T.latin hip hop]                                                          -1.0843      1.007     -1.076      0.282      -3.059       0.890
energy:I(energy ** 3):playlist_subgenre[T.latin pop]                                                               1.1458      0.839      1.366      0.172      -0.498       2.790
energy:I(energy ** 3):playlist_subgenre[T.neo soul]                                                                0.4695      0.765      0.614      0.539      -1.029       1.968
energy:I(energy ** 3):playlist_subgenre[T.new jack swing]                                                         -0.1113      0.930     -0.120      0.905      -1.935       1.712
energy:I(energy ** 3):playlist_subgenre[T.permanent wave]                                                          0.4380      0.751      0.583      0.560      -1.034       1.910
energy:I(energy ** 3):playlist_subgenre[T.pop edm]                                                                 0.4824      1.272      0.379      0.704      -2.010       2.975
energy:I(energy ** 3):playlist_subgenre[T.post-teen pop]                                                           0.1193      0.821      0.145      0.884      -1.489       1.728
energy:I(energy ** 3):playlist_subgenre[T.progressive electro house]                                               0.9480      1.072      0.885      0.376      -1.152       3.048
energy:I(energy ** 3):playlist_subgenre[T.reggaeton]                                                              -5.5372      2.295     -2.412      0.016     -10.036      -1.038
energy:I(energy ** 3):playlist_subgenre[T.southern hip hop]                                                        1.2382      1.097      1.129      0.259      -0.912       3.388
energy:I(energy ** 3):playlist_subgenre[T.trap]                                                                   -0.3119      1.075     -0.290      0.772      -2.418       1.795
energy:I(energy ** 3):playlist_subgenre[T.tropical]                                                                0.1457      0.776      0.188      0.851      -1.375       1.667
energy:I(energy ** 3):playlist_subgenre[T.urban contemporary]                                                      0.0157      0.772      0.020      0.984      -1.497       1.528
I(energy ** 2):I(energy ** 3)                                                                                     -0.0199      0.092     -0.216      0.829      -0.201       0.161
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.big room]                                                       -0.5195      0.803     -0.647      0.518      -2.094       1.055
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.classic rock]                                                   -0.3620      0.206     -1.760      0.078      -0.765       0.041
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.dance pop]                                                       0.2765      0.189      1.464      0.143      -0.094       0.647
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.electro house]                                                   0.0037      0.193      0.019      0.985      -0.374       0.381
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.electropop]                                                     -0.1909      0.155     -1.231      0.218      -0.495       0.113
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.gangster rap]                                                    0.4430      0.292      1.518      0.129      -0.129       1.015
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.hard rock]                                                       0.2149      0.223      0.962      0.336      -0.223       0.653
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.hip hop]                                                         0.1145      0.119      0.965      0.335      -0.118       0.347
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.hip pop]                                                        -0.0167      0.188     -0.089      0.929      -0.385       0.352
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.indie poptimism]                                                 0.1170      0.126      0.926      0.354      -0.131       0.365
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.latin hip hop]                                                  -0.1489      0.236     -0.630      0.528      -0.612       0.314
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.latin pop]                                                       0.2026      0.147      1.376      0.169      -0.086       0.491
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.neo soul]                                                        0.0613      0.124      0.494      0.621      -0.182       0.304
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.new jack swing]                                                  0.1060      0.187      0.567      0.570      -0.260       0.472
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.permanent wave]                                                  0.0982      0.126      0.779      0.436      -0.149       0.345
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.pop edm]                                                         0.1666      0.394      0.423      0.672      -0.606       0.939
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.post-teen pop]                                                   0.0249      0.141      0.176      0.860      -0.251       0.301
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.progressive electro house]                                       0.7693      0.661      1.164      0.245      -0.526       2.065
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.reggaeton]                                                      -4.0745      1.770     -2.302      0.021      -7.545      -0.604
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.southern hip hop]                                                0.3327      0.300      1.109      0.267      -0.255       0.921
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.trap]                                                           -0.0260      0.277     -0.094      0.925      -0.570       0.518
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.tropical]                                                        0.0487      0.126      0.386      0.700      -0.199       0.296
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.urban contemporary]                                              0.0066      0.121      0.055      0.956      -0.230       0.243
valence:I(valence ** 2)                                                                                           -0.4365      0.780     -0.559      0.576      -1.966       1.093
valence:I(valence ** 2):playlist_subgenre[T.big room]                                                              1.2427      1.083      1.148      0.251      -0.880       3.365
valence:I(valence ** 2):playlist_subgenre[T.classic rock]                                                         -0.4502      1.209     -0.373      0.709      -2.819       1.919
valence:I(valence ** 2):playlist_subgenre[T.dance pop]                                                            -0.7714      1.083     -0.712      0.476      -2.894       1.351
valence:I(valence ** 2):playlist_subgenre[T.electro house]                                                        -0.0741      0.980     -0.076      0.940      -1.995       1.847
valence:I(valence ** 2):playlist_subgenre[T.electropop]                                                            0.0723      1.051      0.069      0.945      -1.988       2.133
valence:I(valence ** 2):playlist_subgenre[T.gangster rap]                                                          0.0234      1.023      0.023      0.982      -1.982       2.029
valence:I(valence ** 2):playlist_subgenre[T.hard rock]                                                             0.9972      1.129      0.883      0.377      -1.216       3.211
valence:I(valence ** 2):playlist_subgenre[T.hip hop]                                                               1.8362      1.050      1.748      0.080      -0.222       3.895
valence:I(valence ** 2):playlist_subgenre[T.hip pop]                                                               1.1960      1.204      0.994      0.320      -1.163       3.555
valence:I(valence ** 2):playlist_subgenre[T.indie poptimism]                                                       0.3733      0.998      0.374      0.708      -1.583       2.329
valence:I(valence ** 2):playlist_subgenre[T.latin hip hop]                                                         1.4700      1.186      1.239      0.215      -0.855       3.795
valence:I(valence ** 2):playlist_subgenre[T.latin pop]                                                             0.6063      1.207      0.502      0.615      -1.760       2.973
valence:I(valence ** 2):playlist_subgenre[T.neo soul]                                                             -0.0436      1.056     -0.041      0.967      -2.114       2.026
valence:I(valence ** 2):playlist_subgenre[T.new jack swing]                                                        1.6914      1.399      1.209      0.227      -1.051       4.434
valence:I(valence ** 2):playlist_subgenre[T.permanent wave]                                                        1.0159      1.156      0.879      0.380      -1.250       3.282
valence:I(valence ** 2):playlist_subgenre[T.pop edm]                                                               0.9962      1.113      0.895      0.371      -1.186       3.178
valence:I(valence ** 2):playlist_subgenre[T.post-teen pop]                                                         0.0588      1.221      0.048      0.962      -2.335       2.452
valence:I(valence ** 2):playlist_subgenre[T.progressive electro house]                                             0.2106      0.963      0.219      0.827      -1.677       2.099
valence:I(valence ** 2):playlist_subgenre[T.reggaeton]                                                            -2.0878      1.896     -1.101      0.271      -5.804       1.629
valence:I(valence ** 2):playlist_subgenre[T.southern hip hop]                                                      0.7320      1.056      0.693      0.488      -1.338       2.802
valence:I(valence ** 2):playlist_subgenre[T.trap]                                                                  0.8263      1.045      0.791      0.429      -1.222       2.875
valence:I(valence ** 2):playlist_subgenre[T.tropical]                                                             -1.2864      1.049     -1.226      0.220      -3.343       0.771
valence:I(valence ** 2):playlist_subgenre[T.urban contemporary]                                                    1.3076      1.044      1.253      0.210      -0.738       3.353
valence:I(valence ** 3)                                                                                           -0.1137      0.548     -0.207      0.836      -1.188       0.961
valence:I(valence ** 3):playlist_subgenre[T.big room]                                                              2.7449      1.426      1.925      0.054      -0.050       5.540
valence:I(valence ** 3):playlist_subgenre[T.classic rock]                                                         -0.2669      0.741     -0.360      0.719      -1.720       1.186
valence:I(valence ** 3):playlist_subgenre[T.dance pop]                                                             0.5614      0.771      0.728      0.466      -0.950       2.072
valence:I(valence ** 3):playlist_subgenre[T.electro house]                                                         0.6695      0.790      0.847      0.397      -0.879       2.218
valence:I(valence ** 3):playlist_subgenre[T.electropop]                                                           -0.0683      0.754     -0.091      0.928      -1.546       1.409
valence:I(valence ** 3):playlist_subgenre[T.gangster rap]                                                          1.1263      0.806      1.397      0.163      -0.454       2.707
valence:I(valence ** 3):playlist_subgenre[T.hard rock]                                                            -0.7062      0.860     -0.822      0.411      -2.391       0.979
valence:I(valence ** 3):playlist_subgenre[T.hip hop]                                                              -0.2267      0.771     -0.294      0.769      -1.738       1.285
valence:I(valence ** 3):playlist_subgenre[T.hip pop]                                                               0.3944      0.873      0.452      0.652      -1.318       2.106
valence:I(valence ** 3):playlist_subgenre[T.indie poptimism]                                                       0.5468      0.792      0.691      0.490      -1.005       2.099
valence:I(valence ** 3):playlist_subgenre[T.latin hip hop]                                                        -0.4390      0.731     -0.601      0.548      -1.871       0.993
valence:I(valence ** 3):playlist_subgenre[T.latin pop]                                                             0.0181      0.736      0.025      0.980      -1.425       1.461
valence:I(valence ** 3):playlist_subgenre[T.neo soul]                                                             -0.2401      0.751     -0.320      0.749      -1.712       1.232
valence:I(valence ** 3):playlist_subgenre[T.new jack swing]                                                       -0.2876      0.800     -0.359      0.719      -1.856       1.281
valence:I(valence ** 3):playlist_subgenre[T.permanent wave]                                                       -0.3514      0.773     -0.454      0.649      -1.867       1.164
valence:I(valence ** 3):playlist_subgenre[T.pop edm]                                                              -0.0179      0.876     -0.020      0.984      -1.735       1.699
valence:I(valence ** 3):playlist_subgenre[T.post-teen pop]                                                         0.5031      0.794      0.634      0.526      -1.053       2.059
valence:I(valence ** 3):playlist_subgenre[T.progressive electro house]                                             0.1620      0.786      0.206      0.837      -1.380       1.703
valence:I(valence ** 3):playlist_subgenre[T.reggaeton]                                                            -2.1601      1.177     -1.835      0.067      -4.468       0.148
valence:I(valence ** 3):playlist_subgenre[T.southern hip hop]                                                      0.1527      0.730      0.209      0.834      -1.278       1.583
valence:I(valence ** 3):playlist_subgenre[T.trap]                                                                  1.4775      0.880      1.679      0.093      -0.247       3.202
valence:I(valence ** 3):playlist_subgenre[T.tropical]                                                              0.5104      0.750      0.681      0.496      -0.959       1.980
valence:I(valence ** 3):playlist_subgenre[T.urban contemporary]                                                   -0.2287      0.768     -0.298      0.766      -1.734       1.277
I(valence ** 2):I(valence ** 3)                                                                                    0.1119      0.373      0.300      0.764      -0.620       0.844
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.big room]                                                      0.7091      0.622      1.139      0.255      -0.511       1.929
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.classic rock]                                                  0.3554      0.578      0.615      0.539      -0.778       1.489
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.dance pop]                                                     0.4603      0.531      0.867      0.386      -0.580       1.501
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.electro house]                                                 0.1278      0.482      0.265      0.791      -0.816       1.072
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.electropop]                                                    0.0242      0.507      0.048      0.962      -0.969       1.018
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.gangster rap]                                                  0.1846      0.504      0.367      0.714      -0.802       1.172
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.hard rock]                                                    -0.5065      0.577     -0.877      0.380      -1.638       0.625
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.hip hop]                                                      -0.6023      0.512     -1.177      0.239      -1.606       0.401
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.hip pop]                                                      -0.3335      0.591     -0.564      0.572      -1.492       0.825
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.indie poptimism]                                               0.0988      0.499      0.198      0.843      -0.880       1.078
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.latin hip hop]                                                -0.7236      0.559     -1.295      0.195      -1.819       0.372
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.latin pop]                                                    -0.2676      0.572     -0.468      0.640      -1.389       0.854
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.neo soul]                                                     -0.0121      0.519     -0.023      0.981      -1.030       1.006
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.new jack swing]                                               -0.4331      0.667     -0.649      0.516      -1.740       0.874
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.permanent wave]                                               -0.3998      0.549     -0.728      0.466      -1.476       0.676
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.pop edm]                                                      -0.2292      0.553     -0.415      0.678      -1.313       0.854
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.post-teen pop]                                                 0.3031      0.598      0.507      0.612      -0.868       1.475
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.progressive electro house]                                    -0.0968      0.472     -0.205      0.837      -1.021       0.828
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.reggaeton]                                                     1.2649      1.039      1.217      0.224      -0.772       3.302
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.southern hip hop]                                             -0.1865      0.513     -0.364      0.716      -1.192       0.819
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.trap]                                                          0.1868      0.530      0.353      0.724      -0.851       1.225
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.tropical]                                                      0.5160      0.498      1.036      0.300      -0.460       1.492
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.urban contemporary]                                           -0.4358      0.502     -0.868      0.385      -1.420       0.548
tempo:I(tempo ** 2)                                                                                                0.0515      0.125      0.411      0.681      -0.194       0.297
tempo:I(tempo ** 2):playlist_subgenre[T.big room]                                                                 -0.3281      1.241     -0.264      0.792      -2.761       2.105
tempo:I(tempo ** 2):playlist_subgenre[T.classic rock]                                                             -0.3419      0.315     -1.087      0.277      -0.959       0.275
tempo:I(tempo ** 2):playlist_subgenre[T.dance pop]                                                                -0.0782      0.358     -0.219      0.827      -0.779       0.623
tempo:I(tempo ** 2):playlist_subgenre[T.electro house]                                                            -0.0251      0.783     -0.032      0.974      -1.561       1.510
tempo:I(tempo ** 2):playlist_subgenre[T.electropop]                                                               -0.3229      0.478     -0.675      0.500      -1.260       0.614
tempo:I(tempo ** 2):playlist_subgenre[T.gangster rap]                                                             -0.2686      0.314     -0.855      0.393      -0.884       0.347
tempo:I(tempo ** 2):playlist_subgenre[T.hard rock]                                                                -0.4763      0.490     -0.973      0.331      -1.436       0.483
tempo:I(tempo ** 2):playlist_subgenre[T.hip hop]                                                                  -0.0762      0.196     -0.388      0.698      -0.461       0.309
tempo:I(tempo ** 2):playlist_subgenre[T.hip pop]                                                                   0.3039      0.333      0.913      0.361      -0.348       0.956
tempo:I(tempo ** 2):playlist_subgenre[T.indie poptimism]                                                          -0.5295      0.365     -1.450      0.147      -1.245       0.186
tempo:I(tempo ** 2):playlist_subgenre[T.latin hip hop]                                                             0.1006      0.322      0.313      0.754      -0.530       0.731
tempo:I(tempo ** 2):playlist_subgenre[T.latin pop]                                                                -0.2120      0.442     -0.479      0.632      -1.079       0.655
tempo:I(tempo ** 2):playlist_subgenre[T.neo soul]                                                                 -0.0467      0.224     -0.209      0.835      -0.485       0.392
tempo:I(tempo ** 2):playlist_subgenre[T.new jack swing]                                                            0.1271      0.518      0.245      0.806      -0.889       1.143
tempo:I(tempo ** 2):playlist_subgenre[T.permanent wave]                                                           -0.1062      0.278     -0.382      0.702      -0.650       0.438
tempo:I(tempo ** 2):playlist_subgenre[T.pop edm]                                                                  -0.0419      0.530     -0.079      0.937      -1.081       0.997
tempo:I(tempo ** 2):playlist_subgenre[T.post-teen pop]                                                             0.0994      0.460      0.216      0.829      -0.802       1.001
tempo:I(tempo ** 2):playlist_subgenre[T.progressive electro house]                                                 0.0730      1.332      0.055      0.956      -2.539       2.684
tempo:I(tempo ** 2):playlist_subgenre[T.reggaeton]                                                                -0.7172      0.649     -1.106      0.269      -1.989       0.554
tempo:I(tempo ** 2):playlist_subgenre[T.southern hip hop]                                                         -0.1978      0.282     -0.702      0.483      -0.751       0.355
tempo:I(tempo ** 2):playlist_subgenre[T.trap]                                                                      0.7734      0.654      1.183      0.237      -0.508       2.055
tempo:I(tempo ** 2):playlist_subgenre[T.tropical]                                                                 -0.7687      0.528     -1.455      0.146      -1.804       0.267
tempo:I(tempo ** 2):playlist_subgenre[T.urban contemporary]                                                        0.1227      0.358      0.343      0.732      -0.580       0.825
tempo:I(tempo ** 3)                                                                                                0.2347      0.171      1.375      0.169      -0.100       0.569
tempo:I(tempo ** 3):playlist_subgenre[T.big room]                                                                 -0.4131      0.512     -0.807      0.420      -1.417       0.591
tempo:I(tempo ** 3):playlist_subgenre[T.classic rock]                                                             -0.1490      0.256     -0.581      0.561      -0.652       0.354
tempo:I(tempo ** 3):playlist_subgenre[T.dance pop]                                                                -0.3810      0.307     -1.240      0.215      -0.983       0.221
tempo:I(tempo ** 3):playlist_subgenre[T.electro house]                                                            -0.3815      0.347     -1.100      0.271      -1.061       0.298
tempo:I(tempo ** 3):playlist_subgenre[T.electropop]                                                               -0.6412      0.274     -2.340      0.019      -1.178      -0.104
tempo:I(tempo ** 3):playlist_subgenre[T.gangster rap]                                                             -0.2395      0.260     -0.923      0.356      -0.749       0.269
tempo:I(tempo ** 3):playlist_subgenre[T.hard rock]                                                                -0.5725      0.281     -2.035      0.042      -1.124      -0.021
tempo:I(tempo ** 3):playlist_subgenre[T.hip hop]                                                                  -0.1286      0.235     -0.547      0.585      -0.590       0.333
tempo:I(tempo ** 3):playlist_subgenre[T.hip pop]                                                                  -0.4522      0.280     -1.614      0.107      -1.001       0.097
tempo:I(tempo ** 3):playlist_subgenre[T.indie poptimism]                                                           0.2957      0.244      1.211      0.226      -0.183       0.774
tempo:I(tempo ** 3):playlist_subgenre[T.latin hip hop]                                                            -0.1470      0.211     -0.697      0.486      -0.560       0.266
tempo:I(tempo ** 3):playlist_subgenre[T.latin pop]                                                                -0.4544      0.255     -1.783      0.075      -0.954       0.045
tempo:I(tempo ** 3):playlist_subgenre[T.neo soul]                                                                 -0.3703      0.235     -1.578      0.115      -0.830       0.090
tempo:I(tempo ** 3):playlist_subgenre[T.new jack swing]                                                           -0.2693      0.263     -1.024      0.306      -0.785       0.246
tempo:I(tempo ** 3):playlist_subgenre[T.permanent wave]                                                           -0.2888      0.262     -1.102      0.271      -0.803       0.225
tempo:I(tempo ** 3):playlist_subgenre[T.pop edm]                                                                  -0.1193      0.310     -0.385      0.700      -0.727       0.488
tempo:I(tempo ** 3):playlist_subgenre[T.post-teen pop]                                                            -0.7607      0.281     -2.705      0.007      -1.312      -0.209
tempo:I(tempo ** 3):playlist_subgenre[T.progressive electro house]                                                -0.2251      0.735     -0.306      0.759      -1.666       1.216
tempo:I(tempo ** 3):playlist_subgenre[T.reggaeton]                                                                -0.0292      0.296     -0.099      0.921      -0.609       0.551
tempo:I(tempo ** 3):playlist_subgenre[T.southern hip hop]                                                          0.2172      0.233      0.930      0.352      -0.240       0.675
tempo:I(tempo ** 3):playlist_subgenre[T.trap]                                                                     -0.1845      0.367     -0.503      0.615      -0.904       0.535
tempo:I(tempo ** 3):playlist_subgenre[T.tropical]                                                                  0.0844      0.329      0.257      0.798      -0.560       0.729
tempo:I(tempo ** 3):playlist_subgenre[T.urban contemporary]                                                       -0.0559      0.245     -0.228      0.820      -0.536       0.424
I(tempo ** 2):I(tempo ** 3)                                                                                        0.0125      0.008      1.541      0.123      -0.003       0.028
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.big room]                                                          0.1114      0.429      0.259      0.795      -0.730       0.953
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.classic rock]                                                      0.0703      0.069      1.012      0.312      -0.066       0.207
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.dance pop]                                                        -0.0354      0.087     -0.406      0.685      -0.206       0.135
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.electro house]                                                    -0.0301      0.202     -0.149      0.881      -0.426       0.365
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.electropop]                                                        0.0908      0.139      0.651      0.515      -0.182       0.364
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.gangster rap]                                                      0.0294      0.075      0.391      0.696      -0.118       0.177
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.hard rock]                                                         0.1041      0.159      0.655      0.512      -0.207       0.416
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.hip hop]                                                           0.0095      0.035      0.270      0.787      -0.059       0.078
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.hip pop]                                                          -0.1042      0.074     -1.414      0.157      -0.249       0.040
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.indie poptimism]                                                   0.1657      0.102      1.628      0.104      -0.034       0.365
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.latin hip hop]                                                    -0.0473      0.052     -0.902      0.367      -0.150       0.056
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.latin pop]                                                         0.0035      0.119      0.029      0.977      -0.230       0.237
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.neo soul]                                                         -0.0289      0.046     -0.624      0.533      -0.120       0.062
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.new jack swing]                                                   -0.0277      0.138     -0.201      0.841      -0.298       0.242
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.permanent wave]                                                   -0.0096      0.047     -0.204      0.838      -0.101       0.082
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.pop edm]                                                          -0.0355      0.152     -0.233      0.815      -0.334       0.263
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.post-teen pop]                                                    -0.1161      0.135     -0.861      0.389      -0.381       0.148
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.progressive electro house]                                        -0.2423      0.535     -0.453      0.650      -1.290       0.806
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.reggaeton]                                                         0.0486      0.152      0.320      0.749      -0.249       0.347
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.southern hip hop]                                                  0.0676      0.065      1.043      0.297      -0.059       0.195
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.trap]                                                             -0.3743      0.249     -1.502      0.133      -0.863       0.114
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.tropical]                                                          0.2036      0.163      1.247      0.212      -0.116       0.524
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.urban contemporary]                                               -0.0446      0.094     -0.473      0.636      -0.230       0.140
duration_ms:I(duration_ms ** 2)                                                                                    0.1896      0.105      1.811      0.070      -0.016       0.395
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.big room]                                                     -0.1102      0.711     -0.155      0.877      -1.503       1.283
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.classic rock]                                                 -0.4854      0.322     -1.509      0.131      -1.116       0.145
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.dance pop]                                                    -0.1882      0.504     -0.373      0.709      -1.177       0.801
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.electro house]                                                -0.1405      0.120     -1.168      0.243      -0.376       0.095
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.electropop]                                                    0.3583      0.292      1.226      0.220      -0.215       0.931
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.gangster rap]                                                 -0.3174      0.213     -1.490      0.136      -0.735       0.100
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.hard rock]                                                    -0.1468      0.309     -0.475      0.635      -0.753       0.459
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.hip hop]                                                      -0.1190      0.174     -0.685      0.493      -0.460       0.222
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.hip pop]                                                      -0.2361      0.220     -1.073      0.283      -0.667       0.195
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.indie poptimism]                                              -0.3843      0.492     -0.781      0.435      -1.349       0.580
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.latin hip hop]                                                -0.2322      0.207     -1.123      0.262      -0.637       0.173
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.latin pop]                                                    -0.2180      0.365     -0.597      0.550      -0.934       0.498
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.neo soul]                                                     -0.4898      0.221     -2.213      0.027      -0.924      -0.056
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.new jack swing]                                               -0.4285      0.188     -2.278      0.023      -0.797      -0.060
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.permanent wave]                                                0.2006      0.428      0.469      0.639      -0.638       1.039
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.pop edm]                                                      -0.6275      0.561     -1.119      0.263      -1.727       0.472
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.post-teen pop]                                                -0.6304      0.268     -2.356      0.018      -1.155      -0.106
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.progressive electro house]                                     0.0054      0.283      0.019      0.985      -0.549       0.560
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.reggaeton]                                                     0.3751      0.583      0.643      0.520      -0.767       1.518
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.southern hip hop]                                             -0.2811      0.122     -2.295      0.022      -0.521      -0.041
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.trap]                                                          0.1298      0.412      0.315      0.753      -0.678       0.937
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.tropical]                                                     -0.2456      0.188     -1.308      0.191      -0.614       0.123
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.urban contemporary]                                           -0.5350      0.218     -2.459      0.014      -0.961      -0.109
duration_ms:I(duration_ms ** 3)                                                                                   -0.0175      0.061     -0.286      0.775      -0.138       0.103
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.big room]                                                      0.2683      0.375      0.715      0.475      -0.467       1.004
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.classic rock]                                                 -0.2771      0.187     -1.482      0.138      -0.644       0.089
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.dance pop]                                                     0.0822      0.214      0.383      0.702      -0.338       0.503
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.electro house]                                                 0.0302      0.081      0.374      0.708      -0.128       0.189
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.electropop]                                                   -0.0070      0.115     -0.061      0.951      -0.232       0.218
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.gangster rap]                                                  0.1691      0.187      0.906      0.365      -0.197       0.535
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.hard rock]                                                    -0.0600      0.108     -0.556      0.578      -0.272       0.152
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.hip hop]                                                       0.1048      0.159      0.658      0.511      -0.207       0.417
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.hip pop]                                                      -0.1977      0.211     -0.936      0.349      -0.612       0.216
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.indie poptimism]                                               0.4215      0.253      1.666      0.096      -0.074       0.917
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.latin hip hop]                                                -0.0207      0.102     -0.203      0.839      -0.221       0.179
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.latin pop]                                                    -0.2242      0.301     -0.744      0.457      -0.815       0.367
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.neo soul]                                                     -0.0259      0.102     -0.254      0.800      -0.226       0.174
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.new jack swing]                                                0.1092      0.143      0.765      0.445      -0.171       0.389
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.permanent wave]                                               -0.0732      0.231     -0.318      0.751      -0.525       0.379
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.pop edm]                                                       0.1402      0.242      0.580      0.562      -0.334       0.614
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.post-teen pop]                                                -0.4912      0.260     -1.891      0.059      -1.000       0.018
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.progressive electro house]                                    -0.0996      0.333     -0.299      0.765      -0.753       0.554
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.reggaeton]                                                     0.0351      0.196      0.179      0.858      -0.348       0.419
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.southern hip hop]                                             -0.0830      0.083     -0.996      0.319      -0.246       0.080
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.trap]                                                         -0.2309      0.194     -1.192      0.233      -0.610       0.149
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.tropical]                                                     -0.1163      0.189     -0.614      0.539      -0.487       0.255
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.urban contemporary]                                            0.0156      0.111      0.140      0.888      -0.202       0.233
I(duration_ms ** 2):I(duration_ms ** 3)                                                                           -0.0140      0.014     -1.032      0.302      -0.041       0.013
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.big room]                                              0.0049      0.280      0.018      0.986      -0.545       0.555
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.classic rock]                                          0.1171      0.075      1.568      0.117      -0.029       0.264
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.dance pop]                                             0.0331      0.129      0.257      0.797      -0.219       0.285
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.electro house]                                         0.0144      0.015      0.968      0.333      -0.015       0.044
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.electropop]                                           -0.0736      0.049     -1.516      0.130      -0.169       0.022
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.gangster rap]                                          0.0704      0.049      1.421      0.155      -0.027       0.167
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.hard rock]                                            -0.0023      0.047     -0.049      0.961      -0.095       0.091
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.hip hop]                                               0.0303      0.025      1.205      0.228      -0.019       0.080
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.hip pop]                                              -0.0192      0.041     -0.465      0.642      -0.100       0.062
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.indie poptimism]                                       0.0225      0.152      0.148      0.883      -0.276       0.321
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.latin hip hop]                                         0.0158      0.029      0.545      0.586      -0.041       0.073
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.latin pop]                                            -0.0120      0.080     -0.151      0.880      -0.168       0.144
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.neo soul]                                              0.0513      0.036      1.439      0.150      -0.019       0.121
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.new jack swing]                                        0.0316      0.023      1.355      0.176      -0.014       0.077
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.permanent wave]                                       -0.0897      0.114     -0.784      0.433      -0.314       0.135
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.pop edm]                                               0.1411      0.157      0.899      0.368      -0.166       0.449
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.post-teen pop]                                        -0.0364      0.032     -1.124      0.261      -0.100       0.027
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.progressive electro house]                             0.0242      0.099      0.245      0.807      -0.170       0.219
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.reggaeton]                                            -0.0469      0.121     -0.388      0.698      -0.284       0.190
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.southern hip hop]                                      0.0059      0.015      0.391      0.696      -0.024       0.035
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.trap]                                                  0.0137      0.109      0.126      0.899      -0.199       0.226
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.tropical]                                             -0.0035      0.027     -0.132      0.895      -0.056       0.049
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.urban contemporary]                                    0.0518      0.032      1.622      0.105      -0.011       0.115
artist_hit_rate:I(artist_hit_rate ** 2)                                                                            3.2005      2.885      1.109      0.267      -2.454       8.855
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.big room]                                             -4.7891      8.628     -0.555      0.579     -21.700      12.121
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.classic rock]                                        -10.0471      4.020     -2.499      0.012     -17.927      -2.168
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.dance pop]                                             2.2625      3.708      0.610      0.542      -5.005       9.530
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.electro house]                                        14.4122      7.847      1.837      0.066      -0.969      29.793
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.electropop]                                           -0.3761      3.598     -0.105      0.917      -7.429       6.677
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.gangster rap]                                         -3.7236      3.678     -1.012      0.311     -10.933       3.486
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.hard rock]                                            -0.7139      4.116     -0.173      0.862      -8.781       7.353
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.hip hop]                                              -6.2794      3.910     -1.606      0.108     -13.943       1.384
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.hip pop]                                              -5.1457      4.507     -1.142      0.254     -13.979       3.688
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.indie poptimism]                                     -10.3522      4.116     -2.515      0.012     -18.419      -2.285
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.latin hip hop]                                        -3.7359      4.000     -0.934      0.350     -11.577       4.105
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.latin pop]                                            -2.9068      3.804     -0.764      0.445     -10.362       4.548
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.neo soul]                                             -6.0084      4.542     -1.323      0.186     -14.912       2.895
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.new jack swing]                                       -6.4789     17.730     -0.365      0.715     -41.230      28.272
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.permanent wave]                                        2.5716      3.938      0.653      0.514      -5.147      10.290
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.pop edm]                                              -1.0555      4.403     -0.240      0.811      -9.686       7.575
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.post-teen pop]                                        -2.4475      3.617     -0.677      0.499      -9.538       4.643
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.progressive electro house]                            -5.9912      7.550     -0.794      0.427     -20.789       8.806
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.reggaeton]                                            -2.8819      3.729     -0.773      0.440     -10.191       4.428
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.southern hip hop]                                      7.5348      4.543      1.659      0.097      -1.369      16.439
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.trap]                                                 -5.0470      3.710     -1.360      0.174     -12.318       2.224
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.tropical]                                            -11.3145      4.720     -2.397      0.017     -20.565      -2.064
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.urban contemporary]                                   -1.2146      3.830     -0.317      0.751      -8.721       6.292
artist_hit_rate:I(artist_hit_rate ** 3)                                                                           -2.1489      2.100     -1.023      0.306      -6.265       1.967
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.big room]                                              3.3750      9.631      0.350      0.726     -15.501      22.251
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.classic rock]                                          7.3700      3.033      2.430      0.015       1.425      13.315
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.dance pop]                                            -1.2555      2.591     -0.485      0.628      -6.334       3.823
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.electro house]                                       -13.9100      7.205     -1.931      0.054     -28.032       0.212
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.electropop]                                            0.0341      2.540      0.013      0.989      -4.945       5.013
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.gangster rap]                                          2.7191      2.635      1.032      0.302      -2.446       7.885
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.hard rock]                                             0.8815      3.039      0.290      0.772      -5.075       6.838
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.hip hop]                                               4.5734      2.641      1.732      0.083      -0.602       9.749
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.hip pop]                                               2.9981      3.022      0.992      0.321      -2.925       8.921
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.indie poptimism]                                       6.5831      2.864      2.298      0.022       0.969      12.198
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.latin hip hop]                                         1.9190      2.799      0.686      0.493      -3.568       7.406
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.latin pop]                                             2.0069      2.610      0.769      0.442      -3.108       7.122
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.neo soul]                                              3.7036      3.334      1.111      0.267      -2.831      10.238
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.new jack swing]                                       11.6284     77.192      0.151      0.880    -139.672     162.928
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.permanent wave]                                       -0.8448      2.719     -0.311      0.756      -6.174       4.484
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.pop edm]                                               1.3123      3.083      0.426      0.670      -4.731       7.356
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.post-teen pop]                                         2.1370      2.505      0.853      0.394      -2.773       7.047
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.progressive electro house]                             3.8162      8.628      0.442      0.658     -13.094      20.727
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.reggaeton]                                             1.8413      2.631      0.700      0.484      -3.316       6.998
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.southern hip hop]                                     -8.0530      3.859     -2.087      0.037     -15.617      -0.489
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.trap]                                                  3.7038      2.579      1.436      0.151      -1.352       8.759
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.tropical]                                              8.4015      3.348      2.509      0.012       1.839      14.964
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.urban contemporary]                                    1.3441      2.610      0.515      0.607      -3.771       6.459
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3)                                                                    0.2181      0.234      0.931      0.352      -0.241       0.677
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.big room]                                     -0.2728      1.587     -0.172      0.864      -3.384       2.839
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.classic rock]                                 -0.8068      0.348     -2.317      0.020      -1.489      -0.124
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.dance pop]                                     0.1271      0.283      0.449      0.654      -0.428       0.682
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.electro house]                                 2.0113      1.014      1.983      0.047       0.023       3.999
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.electropop]                                    0.0073      0.279      0.026      0.979      -0.540       0.554
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.gangster rap]                                 -0.2957      0.291     -1.016      0.310      -0.866       0.275
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.hard rock]                                    -0.1196      0.341     -0.350      0.726      -0.789       0.550
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.hip hop]                                      -0.4936      0.283     -1.744      0.081      -1.048       0.061
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.hip pop]                                      -0.2749      0.322     -0.855      0.392      -0.905       0.355
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.indie poptimism]                              -0.6438      0.313     -2.058      0.040      -1.257      -0.031
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.latin hip hop]                                -0.1567      0.306     -0.511      0.609      -0.757       0.444
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.latin pop]                                    -0.2100      0.282     -0.745      0.456      -0.762       0.342
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.neo soul]                                     -0.3653      0.374     -0.977      0.329      -1.098       0.368
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.new jack swing]                               -7.1734     31.250     -0.230      0.818     -68.426      54.079
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.permanent wave]                                0.0478      0.295      0.162      0.871      -0.530       0.626
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.pop edm]                                      -0.1720      0.337     -0.511      0.609      -0.832       0.488
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.post-teen pop]                                -0.2412      0.273     -0.884      0.377      -0.776       0.294
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.progressive electro house]                    -0.4461      1.453     -0.307      0.759      -3.294       2.402
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.reggaeton]                                    -0.1785      0.289     -0.618      0.537      -0.745       0.388
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.southern hip hop]                              1.1793      0.509      2.318      0.020       0.182       2.176
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.trap]                                         -0.3981      0.281     -1.416      0.157      -0.949       0.153
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.tropical]                                     -0.9223      0.369     -2.496      0.013      -1.647      -0.198
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.urban contemporary]                           -0.1595      0.282     -0.567      0.571      -0.711       0.392
artist_n_tracks:I(artist_n_tracks ** 2)                                                                           -1.2427      0.584     -2.128      0.033      -2.387      -0.098
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.big room]                                             -0.2866      0.918     -0.312      0.755      -2.085       1.512
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.classic rock]                                         -0.7137      0.827     -0.863      0.388      -2.334       0.907
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.dance pop]                                             0.7758      0.817      0.950      0.342      -0.825       2.376
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.electro house]                                         1.0229      0.881      1.162      0.245      -0.703       2.749
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.electropop]                                            1.6680      0.802      2.079      0.038       0.096       3.240
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.gangster rap]                                          1.1926      1.049      1.137      0.256      -0.864       3.249
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.hard rock]                                             1.0827      0.825      1.313      0.189      -0.533       2.699
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.hip hop]                                               1.7451      1.230      1.419      0.156      -0.666       4.156
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.hip pop]                                              -1.3331      1.555     -0.857      0.391      -4.380       1.714
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.indie poptimism]                                       3.7295      1.187      3.141      0.002       1.402       6.057
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.latin hip hop]                                         3.2381      0.897      3.610      0.000       1.480       4.996
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.latin pop]                                             0.5250      0.976      0.538      0.590      -1.387       2.437
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.neo soul]                                              1.7630      1.597      1.104      0.270      -1.367       4.893
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.new jack swing]                                        0.2024      1.433      0.141      0.888      -2.607       3.012
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.permanent wave]                                        1.3165      0.948      1.389      0.165      -0.541       3.174
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.pop edm]                                               1.0125      0.935      1.084      0.279      -0.819       2.844
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.post-teen pop]                                         1.2006      0.842      1.426      0.154      -0.450       2.851
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.progressive electro house]                             1.8730      0.827      2.265      0.024       0.252       3.494
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.reggaeton]                                             1.3049      0.991      1.316      0.188      -0.638       3.248
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.southern hip hop]                                      1.4305      0.841      1.701      0.089      -0.217       3.078
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.trap]                                                  0.6050      1.173      0.516      0.606      -1.694       2.904
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.tropical]                                              0.6685      1.385      0.483      0.629      -2.046       3.383
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.urban contemporary]                                    1.5519      1.042      1.489      0.136      -0.491       3.595
artist_n_tracks:I(artist_n_tracks ** 3)                                                                            3.6045      1.598      2.255      0.024       0.472       6.737
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.big room]                                             -4.1255      2.452     -1.683      0.092      -8.931       0.680
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.classic rock]                                         -6.9968      2.297     -3.047      0.002     -11.498      -2.495
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.dance pop]                                            -3.3193      2.221     -1.494      0.135      -7.673       1.034
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.electro house]                                        -4.4930      2.267     -1.982      0.047      -8.936      -0.050
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.electropop]                                           -2.9992      2.168     -1.383      0.167      -7.249       1.250
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.gangster rap]                                         -3.7405      2.516     -1.486      0.137      -8.673       1.192
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.hard rock]                                            -2.2920      2.229     -1.028      0.304      -6.662       2.078
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.hip hop]                                              -2.2987      2.515     -0.914      0.361      -7.227       2.630
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.hip pop]                                              -6.9500      2.937     -2.366      0.018     -12.708      -1.193
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.indie poptimism]                                      -1.7469      2.371     -0.737      0.461      -6.394       2.901
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.latin hip hop]                                        -3.2219      2.346     -1.374      0.170      -7.820       1.376
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.latin pop]                                            -4.5384      2.492     -1.821      0.069      -9.423       0.347
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.neo soul]                                             -2.8045      2.550     -1.100      0.271      -7.803       2.194
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.new jack swing]                                       -4.6840      3.148     -1.488      0.137     -10.854       1.486
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.permanent wave]                                       -3.6405      2.516     -1.447      0.148      -8.572       1.291
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.pop edm]                                              -6.0818      2.449     -2.483      0.013     -10.882      -1.282
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.post-teen pop]                                        -4.3225      2.268     -1.906      0.057      -8.768       0.123
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.progressive electro house]                            -2.2684      2.210     -1.026      0.305      -6.601       2.064
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.reggaeton]                                            -4.9152      2.809     -1.750      0.080     -10.421       0.591
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.southern hip hop]                                     -1.5593      2.206     -0.707      0.480      -5.884       2.765
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.trap]                                                 -4.9515      2.509     -1.974      0.048      -9.869      -0.034
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.tropical]                                             -4.2637      2.665     -1.600      0.110      -9.488       0.960
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.urban contemporary]                                   -3.6677      2.462     -1.490      0.136      -8.493       1.158
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3)                                                                   -0.7902      0.411     -1.923      0.055      -1.596       0.015
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.big room]                                      1.3413      0.777      1.725      0.085      -0.183       2.865
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.classic rock]                                  2.1208      0.630      3.369      0.001       0.887       3.355
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.dance pop]                                     0.7739      0.669      1.156      0.248      -0.538       2.086
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.electro house]                                 1.2556      0.719      1.747      0.081      -0.153       2.664
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.electropop]                                    0.6012      0.623      0.964      0.335      -0.621       1.823
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.gangster rap]                                  0.7290      0.962      0.758      0.449      -1.157       2.615
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.hard rock]                                     0.3877      0.629      0.617      0.538      -0.845       1.620
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.hip hop]                                       0.1114      0.997      0.112      0.911      -1.843       2.066
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.hip pop]                                       2.4837      1.279      1.942      0.052      -0.023       4.990
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.indie poptimism]                              -1.1176      0.959     -1.166      0.244      -2.996       0.761
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.latin hip hop]                                 0.0719      0.747      0.096      0.923      -1.392       1.536
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.latin pop]                                     1.4012      0.838      1.673      0.094      -0.241       3.043
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.neo soul]                                     -0.3598      1.455     -0.247      0.805      -3.211       2.492
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.new jack swing]                                1.5646      1.455      1.075      0.282      -1.288       4.417
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.permanent wave]                                0.8972      0.750      1.196      0.232      -0.573       2.367
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.pop edm]                                       1.7707      0.786      2.254      0.024       0.231       3.310
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.post-teen pop]                                 1.1527      0.652      1.768      0.077      -0.125       2.430
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.progressive electro house]                     0.2297      0.679      0.338      0.735      -1.102       1.561
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.reggaeton]                                     1.2051      0.852      1.414      0.157      -0.465       2.875
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.southern hip hop]                             -0.0603      0.710     -0.085      0.932      -1.452       1.331
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.trap]                                          1.1968      0.994      1.204      0.229      -0.752       3.145
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.tropical]                                      1.0710      1.177      0.910      0.363      -1.236       3.378
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.urban contemporary]                            0.5905      0.906      0.652      0.515      -1.186       2.367
==============================================================================
Omnibus:                     1798.596   Durbin-Watson:                   1.765
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4029.466
Skew:                          -0.413   Prob(JB):                         0.00
Kurtosis:                       4.652   Cond. No.                     2.45e+19
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 3.64e-26. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.

m_8.params.size

1320

m_8.params[m_8.pvalues < 0.05].size

103

m_8.params[m_8.pvalues < 0.05].sort_values(key=abs,ascending=False)

Intercept                                                              29.769541
I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave]   -20.893496
artist_avg_popularity                                                  19.736311
I(playlist_avg_popularity ** 2):playlist_subgenre[T.dance pop]        -15.460021
I(artist_hit_rate ** 2):playlist_subgenre[T.new jack swing]            14.905346
                                                                         ...    
I(artist_avg_popularity ** 3):I(artist_n_tracks ** 3)                   0.070034
I(playlist_avg_popularity ** 3):I(artist_n_tracks ** 3)                -0.063329
I(playlist_avg_popularity ** 3):I(artist_hit_rate ** 3)                -0.035294
I(artist_avg_popularity ** 3):I(playlist_avg_popularity ** 3)          -0.009261
I(playlist_avg_popularity ** 3):I(tempo ** 3)                           0.009132
Length: 103, dtype: float64

m_8.params[m_8.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3]

I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave]   -20.893496
artist_avg_popularity                                                  19.736311
dtype: float64

print(f'R squared: {m_8.rsquared}, RMSE: {m_8.mse_resid**0.5}')

R squared: 0.6473235894945797, RMSE: 14.271722969518153

viz_fitted_vs_actual(m_8.fittedvalues, spotify_model['track_popularity'], 'Most Complex Model')

Best performing model and most complex one. This might come with trade off of out of sample performance.

Prediction

You must predict with the model with ALL inputs and linear additive features.

This corresponds to model 4

f_4

'track_popularity ~ danceability + energy  + speechiness + acousticness + instrumentalness + liveness + valence +     tempo + duration_ms + artist_avg_popularity + artist_hit_rate +     artist_n_tracks + artist_energy_mean + artist_danceability_mean + artist_valence_mean + artist_tempo_mean +     artist_acousticness_mean + artist_speechiness_mean + artist_instrumentalness_mean + artist_liveness_mean+ playlist_avg_popularity + playlist_subgenre + mode  + artist_n_genres + key'

You must identify the continuous input that you feel is the MOST important based on the statistically significant coefficients in your models.

The most important variable in all models is artist_avg_popularity.

The MOST important input must have 101 unique values between the minimum and maximum training set values.

m_4.params[m_4.pvalues < 0.05].sort_values(key=abs,ascending=False)

Intercept                                         41.847548
artist_avg_popularity                             12.773867
playlist_subgenre[T.new jack swing]               -9.898682
playlist_subgenre[T.progressive electro house]    -8.117527
playlist_subgenre[T.big room]                     -7.707655
playlist_subgenre[T.gangster rap]                 -7.379152
playlist_subgenre[T.hard rock]                    -7.049828
playlist_subgenre[T.post-teen pop]                 5.741450
playlist_subgenre[T.pop edm]                      -5.734722
playlist_subgenre[T.neo soul]                     -5.416762
playlist_subgenre[T.electro house]                -5.350412
playlist_subgenre[T.permanent wave]                5.197357
playlist_subgenre[T.southern hip hop]             -5.132238
playlist_subgenre[T.dance pop]                     4.624844
artist_hit_rate                                    4.414877
playlist_subgenre[T.latin hip hop]                -3.553230
artist_n_genres[T.5]                              -3.499970
playlist_subgenre[T.hip hop]                       3.331415
playlist_subgenre[T.classic rock]                 -3.144928
playlist_subgenre[T.tropical]                     -2.329610
playlist_subgenre[T.indie poptimism]              -2.069192
playlist_subgenre[T.electropop]                   -1.467199
instrumentalness                                  -1.425685
artist_n_tracks                                   -1.373468
energy                                            -1.264087
artist_energy_mean                                 1.136957
artist_instrumentalness_mean                       0.981730
artist_valence_mean                               -0.819208
artist_n_genres[T.2]                              -0.676694
danceability                                       0.652449
artist_speechiness_mean                            0.605856
valence                                            0.552617
duration_ms                                       -0.415607
speechiness                                       -0.405382
dtype: float64

viz_1 = pd.DataFrame({'artist_avg_popularity':np.linspace(np.min(spotify_model['artist_avg_popularity']), np.max(spotify_model['artist_avg_popularity']), 101)})

viz_1['playlist_avg_popularity'] = np.mean(spotify_model['playlist_avg_popularity'])
viz_1['danceability'] = np.mean(spotify_model['danceability'])
viz_1['energy'] = np.mean(spotify_model['energy'])
viz_1['speechiness'] = np.mean(spotify_model['speechiness'])
viz_1['acousticness'] = np.mean(spotify_model['acousticness'])
viz_1['instrumentalness'] = np.mean(spotify_model['instrumentalness'])
viz_1['liveness'] = np.mean(spotify_model['liveness'])
viz_1['valence'] = np.mean(spotify_model['valence'])
viz_1['tempo'] = np.mean(spotify_model['tempo'])
viz_1['duration_ms'] = np.mean(spotify_model['duration_ms'])
viz_1['artist_n_tracks'] = np.mean(spotify_model['artist_n_tracks'])
viz_1['artist_hit_rate'] = np.mean(spotify_model['artist_hit_rate'])
viz_1['artist_energy_mean'] = np.mean(spotify_model['artist_energy_mean'])
viz_1['artist_danceability_mean'] = np.mean(spotify_model['artist_danceability_mean'])
viz_1['artist_valence_mean'] = np.mean(spotify_model['artist_valence_mean'])
viz_1['artist_tempo_mean'] = np.mean(spotify_model['artist_tempo_mean'])
viz_1['artist_acousticness_mean'] = np.mean(spotify_model['artist_acousticness_mean'])
viz_1['artist_speechiness_mean'] = np.mean(spotify_model['artist_speechiness_mean'])
viz_1['artist_instrumentalness_mean'] = np.mean(spotify_model['artist_instrumentalness_mean'])
viz_1['artist_liveness_mean'] = np.mean(spotify_model['artist_liveness_mean'])

viz_1['playlist_subgenre'] = spotify_model['playlist_subgenre'].mode()[0]
viz_1['mode'] = spotify_model['mode'].mode()[0]
viz_1['artist_n_genres'] = spotify_model['artist_n_genres'].mode()[0]
viz_1['key'] = spotify_model['key'].mode()[0]

viz_1.nunique()

artist_avg_popularity           101
playlist_avg_popularity           1
danceability                      1
energy                            1
speechiness                       1
acousticness                      1
instrumentalness                  1
liveness                          1
valence                           1
tempo                             1
duration_ms                       1
artist_n_tracks                   1
artist_hit_rate                   1
artist_energy_mean                1
artist_danceability_mean          1
artist_valence_mean               1
artist_tempo_mean                 1
artist_acousticness_mean          1
artist_speechiness_mean           1
artist_instrumentalness_mean      1
artist_liveness_mean              1
playlist_subgenre                 1
mode                              1
artist_n_genres                   1
key                               1
dtype: int64

m_4_pred_summary = m_4.get_prediction(viz_1).summary_frame()
m_4_pred_summary

	mean	mean_se	mean_ci_lower	mean_ci_upper	obs_ci_lower	obs_ci_upper
0	-4.320376	0.668659	-5.630980	-3.009771	-36.103661	27.462910
1	-3.769062	0.664081	-5.070692	-2.467432	-35.551979	28.013855
2	-3.217748	0.659532	-4.510463	-1.925033	-35.000301	28.564805
3	-2.666434	0.655014	-3.950293	-1.382576	-34.448628	29.115759
4	-2.115121	0.650527	-3.390184	-0.840057	-33.896960	29.666719
...	...	...	...	...	...	...
96	48.605744	0.481134	47.662699	49.548789	16.835492	80.375996
97	49.157058	0.482888	48.210574	50.103541	17.386704	80.927412
98	49.708372	0.484719	48.758298	50.658445	17.937911	81.478833
99	50.259685	0.486628	49.305872	51.213499	18.489112	82.030258
100	50.810999	0.488611	49.853298	51.768700	19.040309	82.581689

101 rows × 6 columns

m_8_pred_summary = m_8.get_prediction(viz_1).summary_frame()
m_8_pred_summary

	mean	mean_se	mean_ci_lower	mean_ci_upper	obs_ci_lower	obs_ci_upper
0	6.900155	3.296670	0.438514	13.361797	-22.237119	36.037430
1	7.045006	3.177685	0.816580	13.273432	-22.041438	36.131450
2	7.159484	3.295956	0.699243	13.619725	-21.977480	36.296448
3	7.247127	3.545053	0.298642	14.195611	-22.001965	36.496219
4	7.311287	3.841407	-0.218068	14.840641	-22.081215	36.703788
...	...	...	...	...	...	...
96	77.682430	4.547320	68.769451	86.595409	47.905440	107.459420
97	81.197296	5.314329	70.780940	91.613652	50.936291	111.458301
98	84.892864	6.209965	72.721015	97.064713	53.983612	115.802116
99	88.777785	7.241089	74.584880	102.970690	57.018274	120.537295
100	92.861005	8.415416	76.366361	109.355649	60.008285	125.713726

101 rows × 6 columns

fig, ax = plt.subplots()

ax.fill_between(dfA_viz_b.x2, 
               fit_A_pred_summary_b.obs_ci_lower, fit_A_pred_summary_b.obs_ci_upper,
               facecolor='orange', alpha=0.75, edgecolor='orange')
ax.fill_between(dfA_viz_b.x2,
               fit_A_pred_summary_b.mean_ci_lower, fit_A_pred_summary_b.mean_ci_upper,
               facecolor='grey',edgecolor='grey')

ax.plot(dfA_viz_b.x2, fit_A_pred_summary_b['mean'], color='k',linewidth=1)

ax.set_xlabel('x2')
ax.set_ylabel('y')

plt.show()

# Create visualization for both models
fig, axes = plt.subplots(1, 2, figsize=(15, 6))

# Model 4 (All inputs additive) - Left plot
ax1 = axes[0]

ax1.fill_between(viz_1['artist_avg_popularity'], 
               m_4_pred_summary['obs_ci_lower'], m_4_pred_summary['obs_ci_upper'],
               facecolor='orange', alpha=0.75, edgecolor='orange', label='Prediction Interval (95%)')
ax1.fill_between(viz_1['artist_avg_popularity'],
               m_4_pred_summary['mean_ci_lower'], m_4_pred_summary['mean_ci_upper'],
               facecolor='grey', edgecolor='grey', alpha=0.6, label='Confidence Interval (95%)')

ax1.plot(viz_1['artist_avg_popularity'], m_4_pred_summary['mean'], color='k', linewidth=2, label='Mean Prediction')

ax1.set_xlabel('Artist Average Popularity')
ax1.set_ylabel('Predicted Track Popularity')
ax1.set_title('Model 4: All Inputs Additive')
ax1.legend()
ax1.grid(True, alpha=0.3)

# Model 6 (Artist-Category Interactions) - Right plot
ax2 = axes[1]

ax2.fill_between(viz_1['artist_avg_popularity'], 
               m_8_pred_summary['obs_ci_lower'], m_8_pred_summary['obs_ci_upper'],
               facecolor='orange', alpha=0.75, edgecolor='orange', label='Prediction Interval (95%)')
ax2.fill_between(viz_1['artist_avg_popularity'],
               m_8_pred_summary['mean_ci_lower'], m_8_pred_summary['mean_ci_upper'],
               facecolor='grey', edgecolor='grey', alpha=0.6, label='Confidence Interval (95%)')

ax2.plot(viz_1['artist_avg_popularity'], m_8_pred_summary['mean'], color='k', linewidth=2, label='Mean Prediction')

ax2.set_xlabel('Artist Average Popularity')
ax2.set_ylabel('Predicted Track Popularity')
ax2.set_title('Model 8: Complex Polynomial Interactions')
ax2.legend()
ax2.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

Model 4 is essentially staight line with tighter confidence interval. In constrast, model 7 displays polynomial shape with curvature and more exapnded intervals. Significantly, model 8 does not predict negative track popularity unlike model 4.

You must identify the THREE most important inputs based on the statistically significant coefficients in your models. One of the three must be the SAME input you selected for grid 1. This input will have 101 unique values in the grid 2, just as it did in grid 1. The two other inputs must have fewer unique values in the grid. Categorical inputs should use all unique values (categories). Continuous inputs should use 5 unique values between the training set minimum and maximum values.

viz_2 = pd.DataFrame([
    (x1, x2, x3) 
    for x1 in np.linspace(np.min(spotify_model['artist_avg_popularity']), 
                         np.max(spotify_model['artist_avg_popularity']), num=101)
    for x2 in spotify_model['playlist_subgenre'].unique()
    for x3 in np.linspace(np.min(spotify_model['playlist_avg_popularity']), 
                         np.max(spotify_model['playlist_avg_popularity']), num=5)
], columns=['artist_avg_popularity', 'playlist_subgenre', 'playlist_avg_popularity'])

viz_2 = pd.DataFrame([
    (x1, x2, x3) 
    for x1 in np.linspace(np.min(spotify_model['artist_avg_popularity']), 
                         np.max(spotify_model['artist_avg_popularity']), num=101)
    for x2 in np.linspace(np.min(spotify_model['artist_hit_rate']), 
                         np.max(spotify_model['artist_hit_rate']), num=5)
    for x3 in np.linspace(np.min(spotify_model['playlist_avg_popularity']), 
                         np.max(spotify_model['playlist_avg_popularity']), num=5)
], columns=['artist_avg_popularity', 'artist_hit_rate', 'playlist_avg_popularity'])

viz_2['artist_hit_rate'] = np.mean(spotify_model['artist_hit_rate'])
viz_2['danceability'] = np.mean(spotify_model['danceability'])
viz_2['energy'] = np.mean(spotify_model['energy'])
viz_2['speechiness'] = np.mean(spotify_model['speechiness'])
viz_2['acousticness'] = np.mean(spotify_model['acousticness'])
viz_2['instrumentalness'] = np.mean(spotify_model['instrumentalness'])
viz_2['liveness'] = np.mean(spotify_model['liveness'])
viz_2['valence'] = np.mean(spotify_model['valence'])
viz_2['tempo'] = np.mean(spotify_model['tempo'])
viz_2['duration_ms'] = np.mean(spotify_model['duration_ms'])
viz_2['artist_n_tracks'] = np.mean(spotify_model['artist_n_tracks'])
viz_2['artist_energy_mean'] = np.mean(spotify_model['artist_energy_mean'])
viz_2['artist_danceability_mean'] = np.mean(spotify_model['artist_danceability_mean'])
viz_2['artist_valence_mean'] = np.mean(spotify_model['artist_valence_mean'])
viz_2['artist_tempo_mean'] = np.mean(spotify_model['artist_tempo_mean'])
viz_2['artist_acousticness_mean'] = np.mean(spotify_model['artist_acousticness_mean'])
viz_2['artist_speechiness_mean'] = np.mean(spotify_model['artist_speechiness_mean'])
viz_2['artist_instrumentalness_mean'] = np.mean(spotify_model['artist_instrumentalness_mean'])
viz_2['artist_liveness_mean'] = np.mean(spotify_model['artist_liveness_mean'])

viz_2['mode'] = spotify_model['mode'].mode()[0]
viz_2['artist_n_genres'] = spotify_model['artist_n_genres'].mode()[0]
viz_2['key'] = spotify_model['key'].mode()[0]
viz_2['playlist_subgenre'] = spotify_model['playlist_subgenre'].mode()[0]

viz_2['mode'] = spotify_model['mode'].mode()[0]
viz_2['artist_n_genres'] = spotify_model['artist_n_genres'].mode()[0]
viz_2['key'] = spotify_model['key'].mode()[0]

viz_2.nunique()

artist_avg_popularity           101
playlist_subgenre                24
playlist_avg_popularity           5
artist_hit_rate                   1
danceability                      1
energy                            1
speechiness                       1
acousticness                      1
instrumentalness                  1
liveness                          1
valence                           1
tempo                             1
duration_ms                       1
artist_n_tracks                   1
artist_energy_mean                1
artist_danceability_mean          1
artist_valence_mean               1
artist_tempo_mean                 1
artist_acousticness_mean          1
artist_speechiness_mean           1
artist_instrumentalness_mean      1
artist_liveness_mean              1
mode                              1
artist_n_genres                   1
key                               1
dtype: int64

Make predictions with BOTH models on the visualization grid. You MUST visualize the AVERAGE OUTPUT as a line with respect to the input with the 101 unique values in the visualization grid. The line must be colored by one of the two other inputs with non-constant values. The third input must be associated with the facets. It is your choice as to which input is associated with the line color (hue) versus the facets. If you color by a continuous variable, you should use a diverging color palette. You may use the default color palette for coloring by a categorical variable.

m_4_pred_summary_2 = m_4.get_prediction(viz_2).summary_frame()
m_8_pred_summary_2 = m_8.get_prediction(viz_2).summary_frame()

dfviz2 = pd.DataFrame({
    'artist_avg_popularity': viz_2['artist_avg_popularity'],
    'm4_pred': m_4_pred_summary_2['mean'],
    'm8_pred': m_8_pred_summary_2['mean'],
    'playlist_subgenre': viz_2['playlist_subgenre'],
    'playlist_avg_popularity': viz_2['playlist_avg_popularity']
})

sns.relplot(data=dfviz2, x='artist_avg_popularity', y='m4_pred', hue='playlist_avg_popularity', 
           kind='line', aspect=1.5, col='playlist_subgenre', col_wrap=4,
           facet_kws={'sharey': False})
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

sns.relplot(data=dfviz2,x='artist_avg_popularity',y='m8_pred',row='playlist_subgenre',kind='line',aspect=1.5,col='playlist_avg_popularity', facet_kws={'sharey': False})
plt.show()

d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

The predictions by the two models indciate several things. Model 4 indicates consistent predictions for unseen data. It also shows associates

The more complex model, model 8, on the other hand, contain non linear interactions as indicated by the curved graphs. This is natural as it was constructed with many embedded interactions. However, the model predicts extremely negative values for several subgenres. This indicates potential overfit.

This is not seen with model 4 however. We see more consistent values that are more reasonable. There are some subgenres where track popularity drops below 0 but it is consistent for the most part. This indicates that model 4 will perform better on unforseen data while model 8 already performs much worst.

Models: Performance and Validation

You must select the formulation that was the best model on the training set.

The best formulation was Polynomial Interaction model 7.

You must choose 2 additional formulations. One should be simple (few features), and one should be of medium to high complexity.

Simple model would be continuous only inputs. model 3

Medium complexity is model 5 that has interaction terms between continuous and categoricals.

You must use CROSS-VALIDATION to evaluate the performance for each of the 3 models. Using “regular” K-fold OR stratified K-fold depends on whether you are working on a REGRESSION or CLASSIFICATION problem. You may choose 5-fold, 10-fold, or repeated cross-validation. You must identify an appropriate performance metric to focus on based on the output data type.

from sklearn.linear_model import LinearRegression

from patsy import dmatrices

def fit_and_assess_linearregression(mod_name, a_formula, the_data):
    # create arrays
    y, X = dmatrices(a_formula, data=the_data)
    
    a_mod = LinearRegression(fit_intercept=False).fit( X, y.ravel() )
    
    res_dict = {'model_name': mod_name,
                'model_formula': a_formula,
                'num_coefs': a_mod.coef_.size,
                'R-squared': a_mod.score(X, y.ravel())}
    
    return pd.DataFrame( res_dict, index=[0] )

linearregression_results_list = []
models = [1,2,3,4,5,6,7,8]
for m in models:
    linearregression_results_list.append(
        fit_and_assess_linearregression(f'Model {m}', eval(f'f_{m}'), spotify_model)
    )

linearregression_results_df = pd.concat(linearregression_results_list, ignore_index=True)

linearregression_results_df

	model_name	model_formula	num_coefs	R-squared
0	Model 1	track_popularity ~ 1	1	0.000000
1	Model 2	track_popularity ~ +playlist_subgenre + mode ...	27	0.154829
2	Model 3	track_popularity ~ danceability + energy + sp...	22	0.527651
3	Model 4	track_popularity ~ danceability + energy + sp...	48	0.533418
4	Model 5	track_popularity ~ (danceability + energy + s...	92	0.581912
5	Model 6	track_popularity ~ artist_avg_popularity*(danc...	104	0.585522
6	Model 7	track_popularity ~ (artist_avg_popularity + ...	456	0.623967
7	Model 8	track_popularity ~ (I(artist_avg_popularity*...	780	0.647324

from sklearn.model_selection import KFold

kf = KFold(n_splits=5, shuffle=True, random_state=101)

from sklearn.model_selection import cross_val_score

def lm_cross_val_score(mod_name, a_formula, init_mod, the_data, cv):
    # create the feature and output arrays using the formula
    y, X = dmatrices( a_formula+"-1", data=the_data )
    
    # train and test within each fold - return the test set scores
    # rsquared
    test_r2 = cross_val_score( init_mod, X, y.ravel(), cv=cv )
    # rmse
    test_rmse = -cross_val_score( init_mod, X, y.ravel(), cv=cv, scoring='neg_root_mean_squared_error' )
    
    # book keeping
    res_df=pd.DataFrame({'R-squared': test_r2,
                         'RMSE': test_rmse})
    
    res_df['fold_id'] = res_df.index + 1
    res_df['model_name'] = mod_name
    res_df['model_formula'] = a_formula
    res_df['num_coefs'] = X.shape[1]
    
    return res_df

We retrieve the data before there was any standardization

spotify_model = spotify.copy()
spotify_model = spotify_model.merge(artist_vars, on='track_artist', how='inner')
spotify_model = spotify_model.merge(playlist_vars, on='playlist_id', how='inner')
cont_var = ['danceability', 'energy','speechiness',
    'acousticness', 'instrumentalness', 'liveness', 'valence',
    'tempo', 'duration_ms', 'artist_avg_popularity',
 'artist_n_tracks',
 'artist_hit_rate',
 'artist_energy_mean',
 'artist_danceability_mean',
 'artist_valence_mean',
 'artist_tempo_mean',
 'artist_acousticness_mean',
 'artist_speechiness_mean',
 'artist_instrumentalness_mean',
 'artist_liveness_mean','playlist_avg_popularity']
cat_var = ['playlist_subgenre', 'mode','artist_n_genres', 'key']
spotify_model[cat_var] = spotify_model[cat_var].astype('category')
spotify_model[cont_var] = np.log1p(spotify_model[cont_var])

from sklearn.pipeline import Pipeline

lm = LinearRegression()

# Define the pipeline correctly
lm = LinearRegression()
model_flow = Pipeline([('standardize', StandardScaler()), ('fit', lm)])

# Test it with actual data
y, X = dmatrices(f_4+"-1", data=spotify_model)  # Use an actual formula
z = model_flow.fit(X, y.ravel())
print(f"Pipeline R-squared: {z.score(X, y.ravel())}")

Pipeline R-squared: 0.5339279812076785

model_flow = Pipeline( steps=[ ('standardize', StandardScaler()),('fit', lm) ] )

cv_score_list = []
models = [1,2,3,4,5,6,7,8]
for m in models:
    cv_score_list.append(
        lm_cross_val_score(f'Model {m}', eval(f'f_{m}'), model_flow, spotify_model, kf)
    )

cv_score_df = pd.concat(cv_score_list, ignore_index=True)

sns.catplot(data = cv_score_df, x='model_name', y='R-squared', kind='point', aspect=1.5, join=False,errorbar=('ci',95))
plt.show()

C:\Users\pc\AppData\Local\Temp\ipykernel_15864\2824232948.py:1: UserWarning: 

The `join` parameter is deprecated and will be removed in v0.15.0. You can remove the line between points with `linestyle='none'`.

  sns.catplot(data = cv_score_df, x='model_name', y='R-squared', kind='point', aspect=1.5, join=False,errorbar=('ci',95))
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

sns.catplot(data = cv_score_df, x='model_name', y='RMSE', kind='point', aspect=1.5, join=False,errorbar=('ci',95))
plt.show()

C:\Users\pc\AppData\Local\Temp\ipykernel_15864\632921638.py:1: UserWarning: 

The `join` parameter is deprecated and will be removed in v0.15.0. You can remove the line between points with `linestyle='none'`.

  sns.catplot(data = cv_score_df, x='model_name', y='RMSE', kind='point', aspect=1.5, join=False,errorbar=('ci',95))
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

Which model is the BEST according to CROSS-VALIDATION?

cv_score_df

	R-squared	RMSE	fold_id	model_name	model_formula	num_coefs
0	-0.000662	23.637349	1	Model 1	track_popularity ~ 1	1
1	-0.000082	23.359256	2	Model 1	track_popularity ~ 1	1
2	-0.000968	24.082243	3	Model 1	track_popularity ~ 1	1
3	-0.000061	23.640301	4	Model 1	track_popularity ~ 1	1
4	-0.000023	23.777993	5	Model 1	track_popularity ~ 1	1
5	0.152738	21.750227	1	Model 2	track_popularity ~ +playlist_subgenre + mode ...	40
6	0.159812	21.410636	2	Model 2	track_popularity ~ +playlist_subgenre + mode ...	40
7	0.151861	22.167685	3	Model 2	track_popularity ~ +playlist_subgenre + mode ...	40
8	0.158546	21.684781	4	Model 2	track_popularity ~ +playlist_subgenre + mode ...	40
9	0.157595	21.823817	5	Model 2	track_popularity ~ +playlist_subgenre + mode ...	40
10	0.519846	16.373648	1	Model 3	track_popularity ~ danceability + energy + sp...	22
11	0.529176	16.027670	2	Model 3	track_popularity ~ danceability + energy + sp...	22
12	0.532567	16.456841	3	Model 3	track_popularity ~ danceability + energy + sp...	22
13	0.529141	16.221290	4	Model 3	track_popularity ~ danceability + energy + sp...	22
14	0.523366	16.415829	5	Model 3	track_popularity ~ danceability + energy + sp...	22
15	0.523710	16.307626	1	Model 4	track_popularity ~ danceability + energy + sp...	61
16	0.534520	15.936459	2	Model 4	track_popularity ~ danceability + energy + sp...	61
17	0.537150	16.375966	3	Model 4	track_popularity ~ danceability + energy + sp...	61
18	0.533729	16.142057	4	Model 4	track_popularity ~ danceability + energy + sp...	61
19	0.528999	16.318539	5	Model 4	track_popularity ~ danceability + energy + sp...	61
20	0.568206	15.527209	1	Model 5	track_popularity ~ (danceability + energy + s...	92
21	0.581225	15.115820	2	Model 5	track_popularity ~ (danceability + energy + s...	92
22	0.587461	15.460344	3	Model 5	track_popularity ~ (danceability + energy + s...	92
23	0.584941	15.229818	4	Model 5	track_popularity ~ (danceability + energy + s...	92
24	0.570745	15.578579	5	Model 5	track_popularity ~ (danceability + energy + s...	92
25	0.571844	15.461661	1	Model 6	track_popularity ~ artist_avg_popularity*(danc...	143
26	0.583971	15.066168	2	Model 6	track_popularity ~ artist_avg_popularity*(danc...	143
27	0.590122	15.410406	3	Model 6	track_popularity ~ artist_avg_popularity*(danc...	143
28	0.590970	15.118800	4	Model 6	track_popularity ~ artist_avg_popularity*(danc...	143
29	0.576505	15.473702	5	Model 6	track_popularity ~ artist_avg_popularity*(danc...	143
30	0.597202	14.996806	1	Model 7	track_popularity ~ (artist_avg_popularity + ...	456
31	0.611079	14.567059	2	Model 7	track_popularity ~ (artist_avg_popularity + ...	456
32	0.618149	14.874204	3	Model 7	track_popularity ~ (artist_avg_popularity + ...	456
33	0.607380	14.812420	4	Model 7	track_popularity ~ (artist_avg_popularity + ...	456
34	0.605557	14.933517	5	Model 7	track_popularity ~ (artist_avg_popularity + ...	456
35	0.577814	15.353484	1	Model 8	track_popularity ~ (artist_avg_popularity + ...	1320
36	0.343735	18.922597	2	Model 8	track_popularity ~ (artist_avg_popularity + ...	1320
37	0.469790	17.527131	3	Model 8	track_popularity ~ (artist_avg_popularity + ...	1320
38	-92365.606117	7184.512656	4	Model 8	track_popularity ~ (artist_avg_popularity + ...	1320
39	0.596897	15.096571	5	Model 8	track_popularity ~ (artist_avg_popularity + ...	1320

print(cv_score_df.groupby('model_name')['RMSE'].mean().reset_index().sort_values('RMSE').iloc[0])

model_name      Model 7
RMSE          14.836801
Name: 6, dtype: object

Model 7 has the lowest RMSE and therefore highest R squared. Therefore, it is the best model.

Is this model DIFFERENT from the model identified as the BEST according to the training set?

Yes. Training perforamnce indicated model 7 to be the best.

linearregression_results_df.groupby('model_name')['R-squared'].max().reset_index().sort_values('R-squared', ascending=False).iloc[0].values == cv_score_df.groupby('model_name')['R-squared'].mean().reset_index().sort_values('R-squared').iloc[0]

model_name     True
R-squared     False
Name: 7, dtype: bool

No it was not. Training performance favored the most complex model. In cross validation, the most complext model performed the worst than intercept only model.

How many regression coefficients are associated with the best model?

cv_score_df.groupby(['model_name','num_coefs'])['RMSE'].mean().reset_index().sort_values('RMSE').iloc[0]

model_name      Model 7
num_coefs           456
RMSE          14.836801
Name: 6, dtype: object

There were 456 coefficients.